%   ORIGINAL: 'h4/thm/sum/cond_sum_expand_0'
% 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/INR' x) ('h4/const/sum/INL' y) = 'h4/const/sum/INR' 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/INR' x) ('h4/const/sum/INL' y) = 'h4/const/sum/INR' 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_3f66486,V_3f66482]: ![F, G]: (![X]: s(V_3f66482,happ(s(fun(V_3f66486,V_3f66482),F),s(V_3f66486,X))) = s(V_3f66482,happ(s(fun(V_3f66486,V_3f66482),G),s(V_3f66486,X))) => s(fun(V_3f66486,V_3f66482),F) = s(fun(V_3f66486,V_3f66482),G))).
fof('h4/thm/sum/cond_sum_expand_0', conjecture, ![B,A]: ![P, X, Y, Z]: (s('h4/type/sum/sum'(B,A),'h4/const/bool/COND'(s(bool,P),s('h4/type/sum/sum'(B,A),'h4/const/sum/INR'(s(A,X))),s('h4/type/sum/sum'(B,A),'h4/const/sum/INL'(s(B,Y))))) = s('h4/type/sum/sum'(B,A),'h4/const/sum/INR'(s(A,Z))) <=> (p(s(bool,P)) & s(A,Z) = s(A,X)))).
