Palm Mesocarp Fiber Research Articles

An overview of OPS from oil palm industry as feedstock for bio-oil production

Oil palm industry generates different types of waste biomass in the form of oil palm empty fruit bunch (OPEFB), oil palm mesocarp fibers (OPMF), oil palm fronds (OPF), oil palm trunks (OPT), oil palm bark (OPB), oil palm leaves (OPL), and oil palm shell (OPS). These biomass wastes possess a great energy potential to be converted into biofuels, particularly bio-oil. Among all, the OPS have favorable physicochemical characteristics to be converted into bio-oil. Therefore, this paper mainly focuses to review the suitability of OPS as feedstock for bio-oil production compared to other oil palm biomasses. The physicochemical characteristics of the OPS, in terms of heating value, ultimate analysis, proximate analysis, and lignocellulosic composition, are presented and compared to those of the OPEFB, OPMF, OPF, OPT, OPB, and OPL. To illustrate further and signify the stability, the abovementioned properties of OPS bio-oil are also reviewed and compared to those of bio-oils produced from OPEFB, OPF, OPB, OPL, and petroleum fuels. The challenges and future prospects of OPS as a source of bio-oil are addressed and compared with other wastes of oil palm industry. Additionally, methods used for bio-oil production from oil palm industry biomass are discussed and illustrated in detail.

Upgrading Physicochemical Properties using Torrefaction Process and Anhydrous Weight Loss Modelling for Palm Mesocarp Fiber

Abstract Torrefaction is a thermal process for upgrading biomass properties in order to promote biomass utilization for sustainable energy production. It is performed under inert condition at temperature range 200 - 300°C with residence times between 15 – 60 minutes. Torrefied product usually have high energy content, low moisture content and hygroscopic nature which overcome the limitation of raw biomass as biofuel. Therefore, the objective of this study is to investigate the characteristics of torrefied palm mesocarp fiber (PMF) and evolution of volatiles components during torrefaction at 240°C, 270°C, and 300°C in an inert condition. The condensable and non-condensable gases were analyzed using high performance liquid chromatography (HPLC) and gas chromatography mass spectrometry (GC-MS) respectively. Concurrently, a kinetic model using two reactions in series namely Di Blasi and Lanzetta model is developed to predict the evolution of solid and volatile products during torrefaction process for PMF samples. Based on torrefaction experiments, the mass and energy yields are decreased due to the severe decomposition of biomass at higher temperature but the higher heating value of biomass is increased by 27%. Meanwhile the proximate analysis shows that fixed carbon and ash content are increased by 45% and 25% respectively but volatile matter is decreased by 20%. In addition, the ultimate analysis shows that the elemental ratios of hydrogen to carbon (H/C) and oxygen to carbon (O/C) are decreased by 88% and 20% respectively. For the volatile analysis, 70 – 80% of the total volatile yield is made up from non-condensable gases with high percentage of carbon monoxide (CO) and methane (CH4), while the condensable gases formed was 20-30%. Finally, the anhydrous weight loss model is successfully developed for representing the decomposition of PMF where the kinetic parameters estimated from the model give a good agreement with the residual mass obtained from thermogravimetric analysis.

Effect of Strong Base Buffer on Crude Palm Oil Yield

Abstract Palm oil and its derivatives are widely used in food and oleo chemical industries, and require high yield of crude palm oil (CPO) to fulfill the demand. In palm oil mills, the yield refers to oil extraction rate (OER) that indicates efficiency to squeeze and collect the crude oil from its palm fruit using steam and separation processes. Breakdown of oil cell bearing of mesocarp by the steam may be enhanced by induction of NaOH while the fiber is being digested. The problem of NaOH corrosivity on the steel material of existing unit operations can be controlled by using sodium silicate to form strong base buffer. In this study, the buffer was sprayed on palm mesocarp fiber after 130°C sterilization for 45 min and digestion. The concentration of NaOH in 1 % sodium silicate and dosage of the buffer were applied at 0.8, 1.0 and 3.0 mol/L, and 1, 3 and 5 L/tonne, respectively. Pressing extraction was subsequently followed to imitate the current methods in the mills. The extracted liquid was further clarified by using a centrifuge and produced three layers: oil, water and non-oily solid (NOS). As an indicator to broken cells, concentration of glucose in a mixture of water and NOS was determined using UV-Vis spectroscopy. Oil after centrifuge (OAC) was also recorded. The mesocarp sample treated with the buffer showed improvement of maximum 6.3 wt% of OER and 53.5 wt% of glucose, respectively, implying improvement of oil release using the NaOH buffer.

Utilisation of superheated steam in oil palm biomass pretreatment process for reduced chemical use and enhanced cellulose nanofibre production

In this study, superheated steam (SHS) pretreatment was used as a green approach to partially remove hemicellulose from oil palm mesocarp fibre (OPMF). OPMF was treated with SHS at 260°C for 30 min prior to delignification by NaClO2 to obtain mainly cellulose fibre. Hemicellulose removal by KOH was conducted as a control experiment. Both SHS- and KOH-treated OPMF were later nanofibrillated using a wet disk mill (WDM). The characteristics of CNF produced were analysed in terms of morphological, crystallinity and thermal properties. Based on the chemical compositional analysis, SHS-treated OPMF had residual hemicellulose content of 11% (w/w), and there was no hemicellulose residue in KOH-treated OPMF. The presence of hemicellulose in SHS-treated OPMF was later found to enhance CNF formation during WDM process, whereby it was shown that nanofibrillation of SHS-pretreated OPMF occurred as early as 6th cycle, compared to KOH-pretreated OPMF (8th cycle). This observation could be explained by the presence of hemicellulose which prevented hornification of the cellulose microfibrils during milling process. This finding is significant as not only can the use of chemicals be reduced during pretreatment step, but the use of SHS pretreatment contributed greatly to the productivity of the CNF.

Influence of Oil Content on Solution Load Ethanol-Soda Delignification of Oil Palm Mesocarp Fiber

Mesocarp fiber palm oil industrial waste can be processed into pulp, but this fiber still contains oil with varying levels. The difference oil content in fiber affects the amount of cooking solution required to make mesocarp waste into pulp. This study consists of two stages, namely the pretreatment stage of oil extraction to obtain variations in oil content in the mesocarp fiber waste and the delignification stage using the NaOH-ethanol solution with the ratio of solids:solvent is varied to 1: 8, 1:10 and 1:12. Oil content of the fiber was analyzed, it is consist of 9,5% oil. To vary the oil content, the fibers are soaked in ethanol at room temperature and the levels drop to 7%. And soaking at 40°C can lower the oil content drop to 2%. The obtained pulp had the largest cellulose content 50.77% from delignified product from fiber with 7.6% oil content and solids:solvent ratio: 1:10. While the lowest lignin that was 7.39% obtained at 2.5% oil content. In the delignification process with ratio 1:12, pulp produced is decreased in cellulose content and from FTIR results it is known that it occurs because of the degraded cellulose during the delignification process.

Optimisation studies on the conversion of oil palm biomass to levulinic acid and ethyl levulinate via indium trichloride-ionic liquids: A response surface methodology approach

This work is a continuation and extension of previously published study on the conversions of oil palm empty fruit bunch and mesocarp fiber biomass to levulinic acid and ethyl levulinate via an eco-friendly indium trichloride-1-methylimidazolium hydrogen sulfate (Tiong et al., 2017). Herein, a response surface methodology based on a central composite design method was used to optimise the operating conditions of the conversions. The conversions consisted of a two-sequential steps, that is, depolymerisation to levulinic acid, followed by esterification to ethyl levulinate. The optimum depolymerisation occurred at 177 °C in 4.8 h with 0.15 mmol indium trichloride in ionic liquids-to-biomass ratio of 6.6:1 (w/w) and 22.7% (w/w) of water, whilst esterification was at 105 °C in 12.2 h with ethanol to substrate ratio of 7.2:1 (v/v). The maximum levulinic acid yields of 17.7% and 18.4%, and the subsequent ethyl levulinate yields of 18.7% and 20.1% were achieved from the conversions of oil palm empty fruit bunch and mesocarp fiber biomass, respectively. LA and EL efficiencies were >63% for both biomass conversions. The ionic liquids could be recycled up to three consecutive runs with a minimal loss of <25% of ethyl levulinate yield. This study highlighted the potential of proposed ionic liquids for biorefinery processing of renewable feedstock in a greener and sustainable approach.

THE EFFECT OF PRETREATMENT OF MICROWAVE HEATING ON EFFICIENCY OF HYDROLYSIS TIME AND α-CELLULOSIC CHARACTERISTICS OF PALM OIL WASTE BIOMASS

THE EFFECT OF PRETREATMENT OF MICROWAVE HEATING ON EFFICIENCY OF HYDROLYSIS TIME AND α-CELLULOSIC CHARACTERISTICS OF PALM OIL WASTE BIOMASS. This research is underlied by the needs of various industries for alpha cellulose, especially for the needs of raw material for cellulose nanocristalline, from fiber derived from the most potential waste biomass in Indonesia, namely oil palm empty fruit bunches (OPEFB) and mesocarp fibers. This study aims to find out the effect of pretreatment by microwave heating on the efficiency of hydrolysis time and alpha cellulose characteristics from palm oil waste biomass. To produce alpha cellulose, acid hydrolysis is commonly used with the multistage pulping process method, where the fiber is dissolved into HNO3 mixed acid, 3.5% and NaNO2, heated at a temperature of 90 oC for 2 hours, hydrolyzed and delignified to remove lignin and bleached, then separated from betha and gamma cellulose by dissolving it with NaOH 17.5%. In this study, a preliminary treatment (pretreatment) with microwave heating was carried out before the fiber was hydrolyzed so that the hydrolysis process was more efficient without reducing the characteristics of the alpha cellulose produced. The research results showed that pretreatment with microwave heating can streamline the hydrolysis time from 2 hours to 1 hour, without reducing its characteristics, where the degree of fiber crystallinity (XRD) and the yield of alpha cellulose remain high. Microwave heating with 450 watts for 5 minutes (treatment A) is better than 300 watts of heating for 10 minutes (treatment B). From the results of the study, it can be concluded that the pretreatment with microwave heating can streamline the hydrolysis time of the fiber to obtain alpha cellulose and increase the yield of the produced alpha cellulose.

Effect of SEBS-MA and MAPP as coupling agent on the thermal and mechanical properties in highly filled composites of oil palm fiber/PP

ABSTRACTThis paper reports on a study of highly filled composites of polypropylene (PP) and 75 and 85% by weight of oil palm mesocarp fiber (OPF) with and without coupling agent, maleic anhydride-grafted poly (styrene-ethylene/butadiene styrene) (SEBS-MA) and a maleated polypropylene (MAPP). Composites were prepared using a thermokinetic mixer for blending followed by hot pressing. The thermal and mechanical behavior of these composites was investigated by flexural and impact testing and scanning electron microscopy (SEM). Dynamic mechanical analysis (DMA) was also used to study the properties. The MAPP improve the flexural modulus and flexural strength of the composites with 75 and 85wt% of oil palm fiber while SEBS-MA improved the impact strength of the composites. By SEM it was possible to observe some voids, pull out and debonding in the polypropylene, and allowing the observation of level of adhesion between the fiber and matrix. DMTA showed a decrease in storage modulus when high amounts of fiber were added to polypropylene, however, the presence of the SEBS-MA and MAPP increased the storage modulus. This study looks into the effect of MAH modification on the compatibility of OPF and PP, gives a broad overview of an initial study of these new materials.

Sustainable one-pot process for the production of cellulose nanofiber and polyethylene / cellulose nanofiber composites

Conventional cellulose-based nanocomposites production requires two separate unit operations for the processing: (i) cellulose nanofibrillation unit, and (ii) polymer nanocomposites compounding unit. This two-unit process could be less efficient in terms of energy usage and material handling compared to a one-unit process. Moreover, the present of downtime in between the two steps may affect the overall productivity of the product. In this study, a one-pot process was adapted for nanofibrillation of oil palm mesocarp fiber (OPMF) cellulose and subsequently compounding of the cellulose nanofiber (CNF) with polyethylene (PE) for composites making. Both of these steps were conducted in an extruder with specially-designed twin screw, to allow nanofibrillation and compounding to occur in the same unit. It was interesting to note that CNF produced had diameter range of 80–100 nm, with an aspect ratio of 260. These superior physical properties have led to the excellent mechanical properties of the PE/OPMF-CNF nanocomposites, whereby PE/OPMF-CNF (3 wt%) recorded an increment of 57 and 198% for tensile strength and flexural strength, respectively, compared to the neat PE. Homogeneous dispersion of CNF in the PE matrix was also observed, suggesting the suitability of the one-pot processing method for cellulose-based nanocomposites production. Overall performance of the nanocomposites was similar to that prepared in a two-pot process; with the one-pot process was almost doubled in the productivity compared to two-pot process. A two-step in one unit operation (2-in-1) would be an ideal process for nanocomposites making as this method may improve productivity, reduce downtime in between the two steps, could contribute to a lower capital and processing costs, and may have lower energy consumption. The one-pot process meets most of the green chemistry principles; suggesting the method as a sustainable and greener method for polymer nanocomposites production.

Effect of raw and chemically treated oil palm mesocarp fibers on thermoplastic cassava starch properties

Composites of thermoplastic cassava starch (TPS) and oil palm mesocarp fibers (OPMF) were prepared using a screw extrusion rheometer. Two types of OPMF were used: raw and alkaline treated oil palm fibers. TPS composites using raw fiber showed an improvement of 193% in the elastic modulus and 153% for maximum stress, while the elongation at break was kept constant when compared to the neat TPS matrix. The high improvement in the mechanical and thermal properties of the TPS matrix by the raw fiber is due to the presence of silica, which influences the interaction of the matrix and OPMF fibers. The present work shows that TPS composites with 10 wt% raw fiber have greater mechanical properties than higher OPMF raw fiber content or alkaline treated fibers and provides the use of OPMF residue to produce an eco-friendly composite for various applications.

One-pot nanofibrillation of cellulose and nanocomposite production in a twin-screw extruder

Oil palm mesocarp fiber (OPMF) is rich in cellulose and suitable to be used as raw material for the production of cellulose nanofiber (CNF) and biocomposite. Recently, there have been reports on the use of CNF as filler in polypropylene (PP) for improving the mechanical properties of PP, however the process requires two steps: (i) nanofibrillation for CNF production and (ii) biocomposite compounding. In this study, a one-pot process was developed whereby nanofibrillation of cellulose and subsequently melt-blending of the CNF with PP were conducted at once, in a twin-screw extruder. Morphological analysis of the biocomposites by SEM showed that the cellulose was successfully fibrillated into CNF and compounded homogeneously with PP. The highest tensile strength, Young’s modulus, flexural strength, and flexural modulus recorded were 34.9 ± 0.5 MPa, 12.1 ± 0.1 GPa, 59.3 ± 1.3 MPa, and 2.3 ± 0.05 GPa, respectively when 3 % CNF was used in the biocomposite. The reinforcement of CNF-OPMF in PP improved the mechanical properties of the biocomposite by 33.4 % compared to neat PP. It is interesting to note that the addition of CNF managed to improve the crystallinity of the biocomposite (54.6 %) compared to neat PP (50.1 %), despite of the lower crystallinity of CNF compared to PP. This observation can be attributed to the high density of covalent bonds per cross-sectional area and the large number of hydrogen bonding sites. Additionally, the observation can be explained by the role of CNF in composite which acted as nucleation agent, which eventually increased the crystallinity of the biocomposite.

Characteristics of cellulose from oil palm mesocarp fibres extracted by multi-step pretreatment methods

Characteristics of cellulose isolated from oil palm mesocarp fiber (OPMF) using multi-step pretreatment methods were determined in this study. It was postulated that the succession of pretreatment steps for cellulose extraction from lignocellulosic biomass may affect the cellulose properties. Pretreatment steps involved in cellulose extraction were superheated steam (SHS) treatment, enzymatic hydrolysis and alkaline treatment. OPMF was subjected to SHS treatment to open up the fibres wall structure followed by enzymatic hydrolysis using xylanase for effectiveness enhancement the alkaline treatment afterwards. In order to obtain bleached cellulose, peracetic acid, a totally chlorine free (TCF) chemical was used. Cellulose obtained from these multi-step pretreatment methods had purity of 87.5 %, with crystallinity of 69.2 % and thermally stable up to 360°C.

Characterization of cellulose nanofiber from oil palm mesocarp fiber produced by ultrasonication

Oil palm mesocarp fibre (OPMF) is one of the major biomass generated from palm oil industry and it is currently inefficiently burnt at palm oil mill for energy and as a mean of disposal. With the growing concern on environmental sustainability and finite supply of non-renewable resources, particular attention has been given to produce value-added materials from OPMF, such as biocomposite and biocompost. Since OPMF contains mainly cellulose, there is high potential for the production of cellulose nanofiber (CNF) from OPMF. In this study, cellulose was obtained from OPMF by chemical extraction. OPMF-cellulose obtained was then soaked in distilled water [0.2 - 1% (w/v)] prior to nanofibrillation using an ultrasonicator at 125 W and 36 kHz for 3 to 12 hours. Scanning electron microscopy (SEM) micrographs of fiber undergone ultrasonication confirmed the occurrence of CNF having diameter in the range of 40-200 nm. CNF produced had crystallinity value in the range of 31-43%, and was thermally stable up to 340 °C.

Kinetic study on oil palm biomass conversion to levulinic acid via indium trichloride-ionic liquids

This study investigates the kinetics of depolymerisation reaction of oil palm mesocarp fiber biomass conversion to levulinic acid via Bronsted-Lewis acidic ionic liquids catalyst. An eco-friendly catalyst was developed by coupling Lewis acid indium trichloride with a noncorrosive acidic mono-alkylated ionic liquids, 1-methylimidazolium hydrogen sulfate, for the production of levulinic acid in a greener perspective. The kinetic experiments were conducted at mild temperatures ranged from 135 to 175°C at varying time of 1.5 to 5h. A kinetic model based on the pseudo first-order reaction was established to describe the behaviour of catalytic LA production. The activation energy of the depolymerisation reaction was calculated to be 61.8 kJ mol-1, which is comparatively lower than the previous reported values via various catalytic means of LA production from various biomass feedstock.

Properties of Cellulose Extract from Different Types of Oil Palm Biomass

This study focuses on the characteristics of cellulose extracts from different oil palm biomass namely oil palm mesocarp fiber (OPMF), oil palm empty fruit bunch (OPEFB) and oil palm frond (OPF). Cellulose was obtained from these biomass through soda pulping process followed by a totally chlorine free (TCF) bleaching step using peracetic acid solution. It was found that the cellulose extract for OPMF, OPEFB and OPF had 88.8%, 93.0% and 94.6% purity. Further analyses on the properties of cellulose in terms of morphology, thermal stability and crystallinity were conducted. The OPF cellulose obtained after pretreatment exhibited the highest crystallinity at 84.5%, followed by OPEFB (82.4%) and OPMF (69.2%). This directly affected the thermal stability of the celluloses, in which OPF cellulose was more thermally stable compared to celluloses from OPEFB and OPMF, as being recorded by a thermogravimetry analyzer (TGA). Results from this study provide new insight not only for fundamental understanding, but also to forecast the potential applications of cellulose extracts from different type of oil palm biomass, based on the performance of the celluloses reported herein.

Subcritical Water-Carbon Dioxide Pretreatment of Oil Palm Mesocarp Fiber for Xylooligosaccharide and Glucose Production.

The present work aimed to investigate the pretreatment of oil palm mesocarp fiber (OPMF) in subcritical H2O-CO2 at a temperature range from 150–200 °C and 20–180 min with CO2 pressure from 3–5 MPa. The pretreated solids and liquids from this process were separated by filtration and characterized. Xylooligosaccharides (XOs), sugar monomers, acids, furans and phenols in the pretreated liquids were analyzed by using HPLC. XOs with a degree of polymerization X2–X4 comprising xylobiose, xylotriose, xylotetraose were analyzed by using HPAEC-PAD. Enzymatic hydrolysis was performed on cellulose-rich pretreated solids to observe xylose and glucose production. An optimal condition for XOs production was achieved at 180 °C, 60 min, 3 MPa and the highest XOs obtained was 81.60 mg/g which corresponded to 36.59% of XOs yield from total xylan of OPMF. The highest xylose and glucose yields obtained from pretreated solids were 29.96% and 84.65%, respectively at cellulase loading of 10 FPU/g-substrate.

Superheated steam pretreatment of cellulose affects its electrospinnability for microfibrillated cellulose production

In this study, oil palm mesocarp fiber (OPMF) was pretreated with (1) superheated steam (SHS) and (2) potassium hydroxide (KOH) to remove hemicellulose. Both SHS–OPMF and KOH–OPMF underwent delignification step to isolate the cellulose and dissolved in selected ionic liquid and its co-solvent before being electrospun to obtain microfibrillated cellulose (MFC). FE-SEM images showed that SHS–OPMF cellulose produced discontinuous MFC fiber with diameter ranging from 100 to 500 nm, of which 15.5% were in the range of 100–200 nm; while KOH–OPMF cellulose produced continuous MFC with sizes larger than 200 nm. The differences in fiber size and continuity of fiber produced were due to incomplete removal of hemicellulose from SHS–OPMF sample that inhibited fiber re-coalescence and resulted in interruption in fiber formation.

Simple Manufacture of Surface-Modified Nanolignocellulose Fiber via Vapor-Phase-Assisted Surface Polymerization.

This work tackles the disadvantages in the production of functionalized nanofibers from biomass and offers a new methodology to nanofiber-reinforced composite manufacturing. A vapor-phase-assisted surface polymerization (VASP) method has been used to develop surface-modified lignocellulosic nanofibers. Through the vaporized monomers during polymerization, the polymer chains can be introduced deep within oil palm mesocarp fibers (OPMFs) due to their unique porous structure. After OPMFs are modified with polymer chains, the simple Mortar grinder mill–ionic liquid (M-IL) method provides fibrillation from the macro- to nanoscale, retaining the grafted polymer chains. This approach for the functionalization of biomass could lead to the large-scale fabrication of surface-modified nanofibers for reinforced materials and promote innovative implementations of the renewable biomass resource.

Combination of Superheated Steam with Laccase Pretreatment Together with Size Reduction to Enhance Enzymatic Hydrolysis of Oil Palm Biomass.

The combination of superheated steam (SHS) with ligninolytic enzyme laccase pretreatment together with size reduction was conducted in order to enhance the enzymatic hydrolysis of oil palm biomass into glucose. The oil palm empty fruit bunch (OPEFB) and oil palm mesocarp fiber (OPMF) were pretreated with SHS and ground using a hammer mill to sizes of 2, 1, 0.5 and 0.25 mm before pretreatment using laccase to remove lignin. This study showed that reduction of size from raw to 0.25 mm plays important role in lignin degradation by laccase that removed 38.7% and 39.6% of the lignin from OPEFB and OPMF, respectively. The subsequent saccharification process of these pretreated OPEFB and OPMF generates glucose yields of 71.5% and 63.0%, which represent a 4.6 and 4.8-fold increase, respectively, as compared to untreated samples. This study showed that the combination of SHS with laccase pretreatment together with size reduction could enhance the glucose yield.

Enhanced lignin extraction from different species of oil palm biomass: Kinetics and optimization of extraction conditions

Lignin from industrial crops is a renewable bioresource which can be used for a variety of value-added applications, however effective separation of lignin from lignocellulosic biomass is still an ongoing challenge. The present study involves the selective extraction of lignins from three different morphological parts of oil palm biomass plant, namely empty fruit bunches (EFB), palm mesocarp fiber (PMF) and palm kernel shells (PKS) using Pyridinium Formate [PyFor], a Protic ionic liquid under mild extraction conditions compared to the conventional chemical processes. The effect of initial lignin contents and parameters (namely, particle size range, extraction temperature, time and solid loading) influencing the lignin extraction efficiency were analyzed and optimized using response surface methodology. The experiments conducted at the estimated optimum conditions gave the maximum lignin extraction of 92.01%, 91.23% and 90.70% at lowest process temperatures 351.5 K, 361.9 K and 370.8 K for EFB, PMF and PKS respectively. In a second-stage the extraction experiments were conducted to study the kinetics of extraction process under selected conditions and results were well correlated using pseudo-second order kinetics model. The theoretical lignin concentration at saturation (Cs), rate constant (K) and initial rate of extraction (h) at various temperatures ranging from 323 to 373 K were determined. The nature of biomass source and initial lignin content were found to have major impact on the extraction kinetics. Furthermore, the present estimated activation energies of 12 kJ mol−1, 23 kJ mol−1 and 28 kJ mol−1 for the present extraction of lignins from EFB, PMF and PKS respectively are remarkably lower as compared to those reported in literature for traditional wood pulp processes. The extracted lignins were successfully characterized using FTIR and 1H NMR analysis. The regeneration and recyclability of [PyFor] is also tested and the sustainability of the solvent for commercial application is proved.