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[2] [3 ] [4] Overfull \hbox (53.39583pt too wide) in paragraph at lines 594--608 \OT1/cmr/m/n/10 Mendelson in-tro-duces the \OT1/cmr/bx/n/10 De-duc-tion The-o-r em \OT1/cmr/m/n/10 for first-order the-o-ries in [[]]| [] Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 632. Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 632. [5] \lgwproofline=\count94 Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 926. Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 926. \lgwproofline=\count95 Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 1214. 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Overfull \hbox (32.50768pt too wide) in paragraph at lines 3117--3189 \OT1/cmr/m/n/10 To prove [][]$[L3\OML/cmm/m/it/10 :\OT1/cmr/m/n/10 2(f)[]]$[][] [][][] us-ing in-duc-tion, we will need to prove the base case [][]$[[][]]$[][] [][][]| [] \lgwproofline=\count104 Underfull \hbox (badness 1521) in paragraph at lines 3323--3323 []$\OT1/cmr/m/n/10 ([] [] [] [] []) [] (([][]: ([] [] [] Underfull \hbox (badness 2027) in paragraph at lines 3323--3323 [] [] [] [] [] [] [] [] []\OT1/cmr/m/n/10 )) [] [] Underfull \hbox (badness 3343) in paragraph at lines 3382--3382 []$\OT1/cmr/m/n/10 ([][]: ([] [] [] [] [] [] [] [] [] Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 3472. 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Package hyperref Warning: Token not allowed in a PDFDocEncoded string, (hyperref) removing `math shift' on input line 7453. \lgwproofline=\count112 Underfull \hbox (badness 7451) in paragraph at lines 7618--7618 []$[][]\OT1/cmr/m/n/10 : ([] [] [] [] ([] [] [])[]) [] [] Underfull \hbox (badness 5475) in paragraph at lines 7735--7735 []$[][]\OT1/cmr/m/n/10 : ([] [] [] [] ([] [] [])[]) [] [] Underfull \hbox (badness 6493) in paragraph at lines 7852--7852 []$[][]\OT1/cmr/m/n/10 : ([] [] [] [] ([] [] [])[]) [] [] Underfull \hbox (badness 10000) in paragraph at lines 7508--7945 [] Underfull \hbox (badness 10000) in paragraph at lines 7508--7945 [] \lgwproofline=\count113 Underfull \hbox (badness 1337) in paragraph at lines 8698--8698 []$[][]\OT1/cmr/m/n/10 : [][]: ([] [] [] [] ([] [] [])[]) [] [] Underfull \hbox (badness 1337) in paragraph at lines 8750--8750 []$[][]\OT1/cmr/m/n/10 : [][]: ([] [] [] [] ([] [] [])[]) [] [] Underfull \hbox (badness 6825) in paragraph at lines 8838--8838 []$[][]\OT1/cmr/m/n/10 : ([] [] [] [] ([] [] [])[]) [] [] [15] [16] [17] [18 ] (./page.aux) ) Here is how much of TeX's memory you used: 2268 strings out of 95835 30752 string characters out of 1195527 108316 words of memory out of 1000001 5195 multiletter control sequences out of 10000+50000 14564 words of font info for 54 fonts, out of 500000 for 1000 14 hyphenation exceptions out of 1000 25i,11n,39p,178b,283s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on page.dvi (18 pages, 121404 bytes).