%   ORIGINAL: 'h4/thm/pair/LET2_RATOR_'
% 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: !M N b. 'h4/const/bool/LET' ('h4/const/pair/UNCURRY' (\x y. N x y)) M b = 'h4/const/bool/LET' ('h4/const/pair/UNCURRY' (\x y. N x y b)) M
%   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: !_3. (!N x b y. happ (happ (happ (happ _3 N) x) b) y = happ (happ (happ N x) y) b) ==> (!_2. (!N b x. happ (happ (happ _2 N) b) x = happ (happ (happ _3 N) x) b) ==> (!_1. (!N x y. happ (happ (happ _1 N) x) y = happ (happ N x) y) ==> (!_0. (!N x. happ (happ _0 N) x = happ (happ _1 N) x) ==> (!M N b. happ ('h4/const/bool/LET' ('h4/const/pair/UNCURRY' (happ _0 N)) M) b = 'h4/const/bool/LET' ('h4/const/pair/UNCURRY' (happ (happ _2 N) b)) M))))
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_3f61486,V_3f61482]: ![F, G]: (![X]: s(V_3f61482,happ(s(fun(V_3f61486,V_3f61482),F),s(V_3f61486,X))) = s(V_3f61482,happ(s(fun(V_3f61486,V_3f61482),G),s(V_3f61486,X))) => s(fun(V_3f61486,V_3f61482),F) = s(fun(V_3f61486,V_3f61482),G))).
fof('h4/thm/pair/LET2_RATOR_', conjecture, ![C,B,A1,A2]: ![V__3]: (![N, X, B0, Y]: s(C,happ(s(fun(A2,C),happ(s(fun(B,fun(A2,C)),happ(s(fun(A1,fun(B,fun(A2,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(A1,fun(B,fun(A2,C)))),V__3),s(fun(A1,fun(A2,fun(B,C))),N))),s(A1,X))),s(B,B0))),s(A2,Y))) = s(C,happ(s(fun(B,C),happ(s(fun(A2,fun(B,C)),happ(s(fun(A1,fun(A2,fun(B,C))),N),s(A1,X))),s(A2,Y))),s(B,B0))) => ![V__2]: (![N, B0, X]: s(fun(A2,C),happ(s(fun(A1,fun(A2,C)),happ(s(fun(B,fun(A1,fun(A2,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(B,fun(A1,fun(A2,C)))),V__2),s(fun(A1,fun(A2,fun(B,C))),N))),s(B,B0))),s(A1,X))) = s(fun(A2,C),happ(s(fun(B,fun(A2,C)),happ(s(fun(A1,fun(B,fun(A2,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(A1,fun(B,fun(A2,C)))),V__3),s(fun(A1,fun(A2,fun(B,C))),N))),s(A1,X))),s(B,B0))) => ![V__1]: (![N, X, Y]: s(fun(B,C),happ(s(fun(A2,fun(B,C)),happ(s(fun(A1,fun(A2,fun(B,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(A1,fun(A2,fun(B,C)))),V__1),s(fun(A1,fun(A2,fun(B,C))),N))),s(A1,X))),s(A2,Y))) = s(fun(B,C),happ(s(fun(A2,fun(B,C)),happ(s(fun(A1,fun(A2,fun(B,C))),N),s(A1,X))),s(A2,Y))) => ![V__0]: (![N, X]: s(fun(A2,fun(B,C)),happ(s(fun(A1,fun(A2,fun(B,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(A1,fun(A2,fun(B,C)))),V__0),s(fun(A1,fun(A2,fun(B,C))),N))),s(A1,X))) = s(fun(A2,fun(B,C)),happ(s(fun(A1,fun(A2,fun(B,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(A1,fun(A2,fun(B,C)))),V__1),s(fun(A1,fun(A2,fun(B,C))),N))),s(A1,X))) => ![M, N, B0]: s(C,happ(s(fun(B,C),'h4/const/bool/LET'(s(fun('h4/type/pair/prod'(A1,A2),fun(B,C)),'h4/const/pair/UNCURRY'(s(fun(A1,fun(A2,fun(B,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(A1,fun(A2,fun(B,C)))),V__0),s(fun(A1,fun(A2,fun(B,C))),N))))),s('h4/type/pair/prod'(A1,A2),M))),s(B,B0))) = s(C,'h4/const/bool/LET'(s(fun('h4/type/pair/prod'(A1,A2),C),'h4/const/pair/UNCURRY'(s(fun(A1,fun(A2,C)),happ(s(fun(B,fun(A1,fun(A2,C))),happ(s(fun(fun(A1,fun(A2,fun(B,C))),fun(B,fun(A1,fun(A2,C)))),V__2),s(fun(A1,fun(A2,fun(B,C))),N))),s(B,B0))))),s('h4/type/pair/prod'(A1,A2),M)))))))).
