theorem :: AOFA_A01:91
for S being non empty non void 1-1-connectives bool-correct 4,1 integer 11,1,1 -array 11 array-correct BoolSignature
for X being non-empty ManySortedSet of the carrier of S
for T being non-empty b2,b1 -terms all_vars_including inheriting_operations free_in_itself vf-free integer-array VarMSAlgebra over S
for C being bool-correct 4,1 integer 11,1,1 -array image of T
for G being basic GeneratorSystem over S,X,T
for I being integer SortSymbol of S
for M being pure Element of the generators of G . (the_array_sort_of S)
for s being Element of C -States the generators of G
for j being Integer st j in dom ((s . (the_array_sort_of S)) . M) & M . (j,I) in the generators of G . I holds
((s . (the_array_sort_of S)) . M) . j = (s . I) . (M . (j,I))