%   ORIGINAL: 'h4/thm/sum/INL_'
% 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: !x. 'h4/const/sum/ISL' x ==> 'h4/const/sum/INL' ('h4/const/sum/OUTL' x) = 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: !x. 'h4/const/sum/ISL' x ==> 'h4/const/sum/INL' ('h4/const/sum/OUTL' x) = 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_3f66336,V_3f66332]: ![F, G]: (![X]: s(V_3f66332,happ(s(fun(V_3f66336,V_3f66332),F),s(V_3f66336,X))) = s(V_3f66332,happ(s(fun(V_3f66336,V_3f66332),G),s(V_3f66336,X))) => s(fun(V_3f66336,V_3f66332),F) = s(fun(V_3f66336,V_3f66332),G))).
fof('h4/thm/sum/INL_', conjecture, ![A,B]: ![X]: (p(s(bool,'h4/const/sum/ISL'(s('h4/type/sum/sum'(A,B),X)))) => s('h4/type/sum/sum'(A,B),'h4/const/sum/INL'(s(A,'h4/const/sum/OUTL'(s('h4/type/sum/sum'(A,B),X))))) = s('h4/type/sum/sum'(A,B),X))).
