let U1, U2 be Universal_Algebra; :: thesis: for h being Function of U1,U2 st U1,U2 are_similar holds
for o being OperSymbol of (MSSign U1) holds (MSAlg h) . (the_result_sort_of o) = h
let h be Function of U1,U2; :: thesis: ( U1,U2 are_similar implies for o being OperSymbol of (MSSign U1) holds (MSAlg h) . (the_result_sort_of o) = h )
assume A1: U1,U2 are_similar ; :: thesis: for o being OperSymbol of (MSSign U1) holds (MSAlg h) . (the_result_sort_of o) = h
set f = MSAlg h;
let o be OperSymbol of (MSSign U1); :: thesis: (MSAlg h) . (the_result_sort_of o) = h
A2: ( the carrier' of (MSSign U1) = dom (signature U1) & the ResultSort of (MSSign U1) = (dom (signature U1)) --> 0 ) by MSUALG_1:def 8;
A3: 0 in {0} by TARSKI:def 1;
thus (MSAlg h) . (the_result_sort_of o) = (MSAlg h) . ( the ResultSort of (MSSign U1) . o) by MSUALG_1:def 2
.= (0 .--> h) . 0 by A1, A2, Def3, Th10
.= h by A3, FUNCOP_1:7 ; :: thesis: verum