let X be non empty countable set ; AOFA_I00:def 23 for T being Subset of (Funcs (X,INT)) ex f being ExecutionFunction of FreeUnivAlgNSG (ECIW-signature,INT-ElemIns), Funcs (X,INT),T st f is Euclidean
let T be Subset of (Funcs (X,INT)); ex f being ExecutionFunction of FreeUnivAlgNSG (ECIW-signature,INT-ElemIns), Funcs (X,INT),T st f is Euclidean
set c = the Enumeration of X;
set f = the INT-Exec of the Enumeration of X,T;
take
the INT-Exec of the Enumeration of X,T
; the INT-Exec of the Enumeration of X,T is Euclidean
thus
the INT-Exec of the Enumeration of X,T is Euclidean
; verum