set A = the non-empty MSAlgebra of S;
set f = I --> the non-empty MSAlgebra of S;
reconsider f = I --> the non-empty MSAlgebra of S as ManySortedSet of I ;
take f ; :: thesis: for i being set st i in I holds
f . i is non-empty MSAlgebra of S
let i be set ; :: thesis: ( i in I implies f . i is non-empty MSAlgebra of S )
assume i in I ; :: thesis: f . i is non-empty MSAlgebra of S
hence f . i is non-empty MSAlgebra of S by FUNCOP_1:7; :: thesis: verum