%   ORIGINAL: 'h4/thm/sum/cond_sum_expand_2'
% 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: !P x y z. 'h4/const/bool/COND' P ('h4/const/sum/INL' x) ('h4/const/sum/INR' y) = 'h4/const/sum/INL' z <=> P /\ z = x
%   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: !P x y z. 'h4/const/bool/COND' P ('h4/const/sum/INL' x) ('h4/const/sum/INR' y) = 'h4/const/sum/INL' z <=> P /\ z = x
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_3f66536,V_3f66532]: ![F0, G]: (![X]: s(V_3f66532,happ(s(fun(V_3f66536,V_3f66532),F0),s(V_3f66536,X))) = s(V_3f66532,happ(s(fun(V_3f66536,V_3f66532),G),s(V_3f66536,X))) => s(fun(V_3f66536,V_3f66532),F0) = s(fun(V_3f66536,V_3f66532),G))).
fof('h4/thm/sum/cond_sum_expand_2', conjecture, ![F,E]: ![P, X, Y, Z]: (s('h4/type/sum/sum'(E,F),'h4/const/bool/COND'(s(bool,P),s('h4/type/sum/sum'(E,F),'h4/const/sum/INL'(s(E,X))),s('h4/type/sum/sum'(E,F),'h4/const/sum/INR'(s(F,Y))))) = s('h4/type/sum/sum'(E,F),'h4/const/sum/INL'(s(E,Z))) <=> (p(s(bool,P)) & s(E,Z) = s(E,X)))).
