%   ORIGINAL: 'h4/thm/bool/bool_case_thm_e1'
% 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: !t1 t2. 'h4/const/bool/COND' F t1 t2 = t2
%   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: !t1 t2. 'h4/const/bool/COND' F t1 t2 = t2
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_3f34978,V_3f34974]: ![F, G]: (![X]: s(V_3f34974,happ(s(fun(V_3f34978,V_3f34974),F),s(V_3f34978,X))) = s(V_3f34974,happ(s(fun(V_3f34978,V_3f34974),G),s(V_3f34978,X))) => s(fun(V_3f34978,V_3f34974),F) = s(fun(V_3f34978,V_3f34974),G))).
fof('h4/thm/bool/bool_case_thm_e1', conjecture, ![A]: ![T1, T2]: s(A,'h4/const/bool/COND'(s(bool,'F'),s(A,T1),s(A,T2))) = s(A,T2)).
