let f be object ; :: thesis: for p being FinSequence holds
( the Arity of (1GateCircStr (p,f)) = (p,f) .--> p & the ResultSort of (1GateCircStr (p,f)) = (p,f) .--> [p,f] )
let p be FinSequence; :: thesis: ( the Arity of (1GateCircStr (p,f)) = (p,f) .--> p & the ResultSort of (1GateCircStr (p,f)) = (p,f) .--> [p,f] )
set S = 1GateCircStr (p,f);
the Arity of (1GateCircStr (p,f)) . [p,f] = p by Def6;
then A1: for x being object st x in {[p,f]} holds
the Arity of (1GateCircStr (p,f)) . x = p by TARSKI:def 1;
A2: the carrier' of (1GateCircStr (p,f)) = {[p,f]} by Def6;
then dom the Arity of (1GateCircStr (p,f)) = {[p,f]} by FUNCT_2:def 1;
hence the Arity of (1GateCircStr (p,f)) = (p,f) .--> p by A1, FUNCOP_1:11; :: thesis: the ResultSort of (1GateCircStr (p,f)) = (p,f) .--> [p,f]
the ResultSort of (1GateCircStr (p,f)) . [p,f] = [p,f] by Def6;
then A3: for x being object st x in {[p,f]} holds
the ResultSort of (1GateCircStr (p,f)) . x = [p,f] by TARSKI:def 1;
dom the ResultSort of (1GateCircStr (p,f)) = {[p,f]} by A2, FUNCT_2:def 1;
hence the ResultSort of (1GateCircStr (p,f)) = (p,f) .--> [p,f] by A3, FUNCOP_1:11; :: thesis: verum