let ti be INT-Expression of A,f; :: thesis: ( ti = gt t1,t2 iff for s being Element of Funcs X,INT holds ti . s = IFGT (t1 . s),(t2 . s),1,0 )
A13: dom t1 = Funcs X,INT by FUNCT_2:def 1;
A14: dom t2 = Funcs X,INT by FUNCT_2:def 1;
A15: dom (gt t1,t2) = (dom t1) /\ (dom t2) by Def6;
hence ( ti = gt t1,t2 implies for s being Element of Funcs X,INT holds ti . s = IFGT (t1 . s),(t2 . s),1,0 ) by A13, A14, Def6; :: thesis: ( ( for s being Element of Funcs X,INT holds ti . s = IFGT (t1 . s),(t2 . s),1,0 ) implies ti = gt t1,t2 )
A16: dom ti = Funcs X,INT by FUNCT_2:def 1;
assume for s being Element of Funcs X,INT holds ti . s = IFGT (t1 . s),(t2 . s),1,0 ; :: thesis: ti = gt t1,t2
then for s being set st s in Funcs X,INT holds
ti . s = IFGT (t1 . s),(t2 . s),1,0 ;
hence ti = gt t1,t2 by A15, A13, A14, A16, Def6; :: thesis: verum