let G1, G2 be _Graph; :: thesis: ( G1 == G2 implies G1 .tChromaticNum() = G2 .tChromaticNum() )
assume A1: G1 == G2 ; :: thesis: G1 .tChromaticNum() = G2 .tChromaticNum()

per cases ( not G1 is loopless or G1 is loopless ) ;

suppose not G1 is loopless ; :: thesis: G1 .tChromaticNum() = G2 .tChromaticNum()

then ( not G1 is loopless & not G2 is loopless ) by A1, GLIB_000:89;
then ( G1 .tChromaticNum() = 0 & G2 .tChromaticNum() = 0 ) ;
hence G1 .tChromaticNum() = G2 .tChromaticNum() ; :: thesis: verum

end;

suppose G1 is loopless ; :: thesis: G1 .tChromaticNum() = G2 .tChromaticNum()

then ( G2 is G1 .tChromaticNum() -tcolorable & ( for c being Cardinal st G2 is c -tcolorable holds
G1 .tChromaticNum() c= c ) ) by A1, Th167, Th186, Th189;
hence G1 .tChromaticNum() = G2 .tChromaticNum() by Th190; :: thesis: verum

end;

end;