let S be non empty non void bool-correct 4,1 integer BoolSignature ; :: thesis: for X being non-empty ManySortedSet of the carrier of S
for T being b₁,S -terms all_vars_including inheriting_operations free_in_itself vf-free integer VarMSAlgebra over S
for C being bool-correct 4,1 integer image of T
for G being basic GeneratorSystem over S,X,T
for I being integer SortSymbol of S
for s being Element of C -States the generators of G holds (\2 (T,I)) value_at (C,s) = 2
let X be non-empty ManySortedSet of the carrier of S; :: thesis: for T being X,S -terms all_vars_including inheriting_operations free_in_itself vf-free integer VarMSAlgebra over S
for C being bool-correct 4,1 integer image of T
for G being basic GeneratorSystem over S,X,T
for I being integer SortSymbol of S
for s being Element of C -States the generators of G holds (\2 (T,I)) value_at (C,s) = 2
let T be X,S -terms all_vars_including inheriting_operations free_in_itself vf-free integer VarMSAlgebra over S; :: thesis: for C being bool-correct 4,1 integer image of T
for G being basic GeneratorSystem over S,X,T
for I being integer SortSymbol of S
for s being Element of C -States the generators of G holds (\2 (T,I)) value_at (C,s) = 2
let C be bool-correct 4,1 integer image of T; :: thesis: for G being basic GeneratorSystem over S,X,T
for I being integer SortSymbol of S
for s being Element of C -States the generators of G holds (\2 (T,I)) value_at (C,s) = 2
let G be basic GeneratorSystem over S,X,T; :: thesis: for I being integer SortSymbol of S
for s being Element of C -States the generators of G holds (\2 (T,I)) value_at (C,s) = 2
let I be integer SortSymbol of S; :: thesis: for s being Element of C -States the generators of G holds (\2 (T,I)) value_at (C,s) = 2
let s be Element of C -States the generators of G; :: thesis: (\2 (T,I)) value_at (C,s) = 2
A1: (\1 (T,I)) value_at (C,s) = 1 by Th37;
thus (\2 (T,I)) value_at (C,s) = ((\1 (T,I)) value_at (C,s)) + ((\1 (T,I)) value_at (C,s)) by Th39
.= 2 by A1, AOFA_A00:55 ; :: thesis: verum