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 u being ManySortedFunction of FreeGen T, the Sorts of C holds (\false T) value_at (C,u) = FALSE
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 u being ManySortedFunction of FreeGen T, the Sorts of C holds (\false T) value_at (C,u) = FALSE
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 u being ManySortedFunction of FreeGen T, the Sorts of C holds (\false T) value_at (C,u) = FALSE
let C be bool-correct 4,1 integer image of T; :: thesis: for u being ManySortedFunction of FreeGen T, the Sorts of C holds (\false T) value_at (C,u) = FALSE
let u be ManySortedFunction of FreeGen T, the Sorts of C; :: thesis: (\false T) value_at (C,u) = FALSE
thus (\false T) value_at (C,u) = \not ((\true T) value_at (C,u)) by Th47
.= 'not' ((\true T) value_at (C,u)) by AOFA_A00:def 32
.= 'not' TRUE by Th46
.= FALSE ; :: thesis: verum