%   ORIGINAL: 'h4/thm/bool/LET_CONG_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !f g M N. M = N /\ (!x. x = N ==> f x = g x) ==> 'h4/const/bool/LET' f M = 'h4/const/bool/LET' g N
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !f g M N. M = N /\ (!x. x = N ==> happ f x = happ g x) ==> 'h4/const/bool/LET' f M = 'h4/const/bool/LET' g N
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f34353,V_3f34349]: ![F, G]: (![X]: s(V_3f34349,happ(s(fun(V_3f34353,V_3f34349),F),s(V_3f34353,X))) = s(V_3f34349,happ(s(fun(V_3f34353,V_3f34349),G),s(V_3f34353,X))) => s(fun(V_3f34353,V_3f34349),F) = s(fun(V_3f34353,V_3f34349),G))).
fof('h4/thm/bool/LET_CONG_', conjecture, ![B,A]: ![F, G, M, N]: ((s(A,M) = s(A,N) & ![X]: (s(A,X) = s(A,N) => s(B,happ(s(fun(A,B),F),s(A,X))) = s(B,happ(s(fun(A,B),G),s(A,X))))) => s(B,'h4/const/bool/LET'(s(fun(A,B),F),s(A,M))) = s(B,'h4/const/bool/LET'(s(fun(A,B),G),s(A,N))))).
