[ [ ( KeywordTok , "module" ) , ( NormalTok , " Reals " ) , ( KeywordTok , "where" ) ] , [] , [ ( NormalTok , " " ) , ( CommentTok , "-- (a set with properties of) the reals" ) ] , [ ( NormalTok , " " ) , ( KeywordTok , "data" ) , ( NormalTok , " \8477 " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( DataTypeTok , "Set" ) , ( NormalTok , " " ) , ( KeywordTok , "where" ) ] , [ ( NormalTok , " r0 " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477" ) ] , [ ( NormalTok , " r1 " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477" ) ] , [ ( NormalTok , " " ) , ( OtherTok , "_" ) , ( NormalTok , "+" ) , ( OtherTok , "_" ) , ( NormalTok , " " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477 " ) , ( OtherTok , "\8594" ) , ( NormalTok , " \8477 " ) , ( OtherTok , "\8594" ) , ( NormalTok , " \8477" ) ] , [] , [ ( NormalTok , " " ) , ( CommentTok , "-- equality" ) ] , [ ( NormalTok , " " ) , ( KeywordTok , "data" ) , ( NormalTok , " " ) , ( OtherTok , "_" ) , ( NormalTok , "==" ) , ( OtherTok , "_" ) , ( NormalTok , " " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477 " ) , ( OtherTok , "\8594" ) , ( NormalTok , " \8477 " ) , ( OtherTok , "\8594" ) , ( NormalTok , " " ) , ( DataTypeTok , "Set" ) , ( NormalTok , " " ) , ( KeywordTok , "where" ) ] , [ ( NormalTok , " AXrefl== " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == r" ) ] , [ ( NormalTok , " AXsymm== " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " s == r" ) ] , [ ( NormalTok , " AXtrans== " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s t" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " s == t " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == t" ) ] , [ ( NormalTok , " AX+0 " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " " ) , ( OtherTok , "(" ) , ( NormalTok , "r + r0" ) , ( OtherTok , ")" ) , ( NormalTok , " == r" ) ] , [ ( NormalTok , " AXsymm+ " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " " ) , ( OtherTok , "(" ) , ( NormalTok , "r + s" ) , ( OtherTok , ")" ) , ( NormalTok , " == " ) , ( OtherTok , "(" ) , ( NormalTok , "s + r" ) , ( OtherTok , ")" ) ] , [ ( NormalTok , " AX+== " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s t" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " " ) , ( OtherTok , "(" ) , ( NormalTok , "r + t" ) , ( OtherTok , ")" ) , ( NormalTok , " == " ) , ( OtherTok , "(" ) , ( NormalTok , "s + t" ) , ( OtherTok , ")" ) ] , [] , [ ( NormalTok , " THM0+ " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == " ) , ( OtherTok , "(" ) , ( NormalTok , "r0 + r" ) , ( OtherTok , ")" ) ] , [ ( NormalTok , " THM0+ " ) , ( OtherTok , "=" ) , ( NormalTok , " AXsymm== " ) , ( OtherTok , "(" ) , ( NormalTok , "AXtrans== AXsymm+ AX+0" ) , ( OtherTok , ")" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AXsymm+ AX+0 r0 + r == r + r0 and r + r0 == r" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AXtrans== so r0 + r == r" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AXsymm== so r == r0 + r" ) ] , [] , [ ( NormalTok , " THM0+alt " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == " ) , ( OtherTok , "(" ) , ( NormalTok , "r0 + r" ) , ( OtherTok , ")" ) ] , [ ( NormalTok , " THM0+alt " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "=" ) , ( NormalTok , " AXsymm== " ) , ( OtherTok , "{" ) , ( NormalTok , "r0 + r" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "((" ) , ( NormalTok , "AXtrans== " ) , ( OtherTok , "{" ) , ( NormalTok , "r0 + r" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r + r0" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "})" ) , ( NormalTok , " " ) , ( OtherTok , "(" ) , ( NormalTok , "AXsymm+ " ) , ( OtherTok , "{" ) , ( NormalTok , "r0" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "})" ) , ( NormalTok , " " ) , ( OtherTok , "(" ) , ( NormalTok , "AX+0 " ) , ( OtherTok , "{" ) , ( NormalTok , "r" ) , ( OtherTok , "}))" ) ] , [] , [ ( NormalTok , " " ) , ( CommentTok , "-- strict partial ordering" ) ] , [ ( NormalTok , " " ) , ( KeywordTok , "data" ) , ( NormalTok , " " ) , ( OtherTok , "_" ) , ( NormalTok , "<" ) , ( OtherTok , "_" ) , ( NormalTok , " " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477 " ) , ( OtherTok , "\8594" ) , ( NormalTok , " \8477 " ) , ( OtherTok , "\8594" ) , ( NormalTok , " " ) , ( DataTypeTok , "Set" ) , ( NormalTok , " " ) , ( KeywordTok , "where" ) ] , [ ( NormalTok , " AXtrans<<< " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s t" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " s < t " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < t" ) ] , [ ( NormalTok , " AX<=< " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s t" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " s == t " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < t" ) ] , [ ( NormalTok , " AX=<< " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s t" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r == s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " s < t " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < t" ) ] , [ ( NormalTok , " AX0<1 " ) , ( OtherTok , ":" ) , ( NormalTok , " r0 < r1" ) ] , [ ( NormalTok , " AX+<< " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "\8704" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r s t" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < s " ) , ( OtherTok , "\8594" ) , ( NormalTok , " " ) , ( OtherTok , "(" ) , ( NormalTok , "r + t" ) , ( OtherTok , ")" ) , ( NormalTok , " < " ) , ( OtherTok , "(" ) , ( NormalTok , "s + t" ) , ( OtherTok , ")" ) ] , [] , [ ( NormalTok , " THM<+1 " ) , ( OtherTok , ":" ) , ( NormalTok , " " ) , ( OtherTok , "{" ) , ( NormalTok , "r " ) , ( OtherTok , ":" ) , ( NormalTok , " \8477" ) , ( OtherTok , "}" ) , ( NormalTok , " " ) , ( OtherTok , "\8594" ) , ( NormalTok , " r < " ) , ( OtherTok , "(" ) , ( NormalTok , "r + r1" ) , ( OtherTok , ")" ) ] , [ ( NormalTok , " THM<+1 " ) , ( OtherTok , "=" ) , ( NormalTok , " AX<=< " ) , ( OtherTok , "(" ) , ( NormalTok , "AX=<< THM0+ " ) , ( OtherTok , "(" ) , ( NormalTok , "AX+<< AX0<1" ) , ( OtherTok , "))" ) , ( NormalTok , " AXsymm+" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AX0<1 0 < 1" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AX<+ % so 0 + r < 1 + r" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AX=<< lem0+ % so r < 1 + r" ) ] , [ ( NormalTok , " " ) , ( CommentTok , "-- AX<=< % AXsymm+ so r < r + 1" ) ] ]