let C be initialized ConstructorSignature; :: thesis: for c being constructor OperSymbol of C
for a being expression of C, an_Adj C
for p being FinSequence of QuasiTerms C st len p = len (the_arity_of c) holds
c -trm p <> (non_op C) term a
let c be constructor OperSymbol of C; :: thesis: for a being expression of C, an_Adj C
for p being FinSequence of QuasiTerms C st len p = len (the_arity_of c) holds
c -trm p <> (non_op C) term a
let a be expression of C, an_Adj C; :: thesis: for p being FinSequence of QuasiTerms C st len p = len (the_arity_of c) holds
c -trm p <> (non_op C) term a
let p be FinSequence of QuasiTerms C; :: thesis: ( len p = len (the_arity_of c) implies c -trm p <> (non_op C) term a )
assume len p = len (the_arity_of c) ; :: thesis: c -trm p <> (non_op C) term a
then c -trm p = [c, the carrier of C] -tree p by Def35;
then A1: (c -trm p) . {} = [c, the carrier of C] by TREES_4:def 4;
assume c -trm p = (non_op C) term a ; :: thesis: contradiction
then c -trm p = [non_op, the carrier of C] -tree <*a*> by Th43;
then [c, the carrier of C] = [non_op, the carrier of C] by A1, TREES_4:def 4;
then c = non_op by XTUPLE_0:1;
hence contradiction by Def11; :: thesis: verum