%   ORIGINAL: 'h4/thm/bool/UNWIND_FORALL_THM2_'
% 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 v. (!x. x = v ==> f x) <=> f v
%   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 v. (!x. x = v ==> happ f x) <=> happ f v
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_3f34903,V_3f34899]: ![F, G]: (![X]: s(V_3f34899,happ(s(fun(V_3f34903,V_3f34899),F),s(V_3f34903,X))) = s(V_3f34899,happ(s(fun(V_3f34903,V_3f34899),G),s(V_3f34903,X))) => s(fun(V_3f34903,V_3f34899),F) = s(fun(V_3f34903,V_3f34899),G))).
fof('h4/thm/bool/UNWIND_FORALL_THM2_', conjecture, ![A]: ![F, V]: (![X]: (s(A,X) = s(A,V) => p(s(bool,happ(s(fun(A,bool),F),s(A,X))))) <=> p(s(bool,happ(s(fun(A,bool),F),s(A,V)))))).
