%   ORIGINAL: 'h4/thm/rich_list/MAP_FST_funs_'
% 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: !funs. 'h4/const/list/MAP' ('h4/const/pair/UNCURRY' (\x. 'h4/const/pair/UNCURRY' (\y z. x))) funs = 'h4/const/list/MAP' 'h4/const/pair/FST' funs
%   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: !_2. (!x z. happ (happ _2 x) z = x) ==> (!_1. (!x y. happ (happ _1 x) y = happ _2 x) ==> (!_0. (!x. happ _0 x = 'h4/const/pair/UNCURRY' (happ _1 x)) ==> (!funs. 'h4/const/list/MAP' ('h4/const/pair/UNCURRY' _0) funs = 'h4/const/list/MAP' 'h4/const/pair/FST' funs)))
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_3f57886,V_3f57882]: ![F, G]: (![X]: s(V_3f57882,happ(s(fun(V_3f57886,V_3f57882),F),s(V_3f57886,X))) = s(V_3f57882,happ(s(fun(V_3f57886,V_3f57882),G),s(V_3f57886,X))) => s(fun(V_3f57886,V_3f57882),F) = s(fun(V_3f57886,V_3f57882),G))).
fof('h4/thm/rich_list/MAP_FST_funs_', conjecture, ![A,B,C]: ![V__2]: (![X, Z]: s(A,happ(s(fun(C,A),happ(s(fun(A,fun(C,A)),V__2),s(A,X))),s(C,Z))) = s(A,X) => ![V__1]: (![X, Y]: s(fun(C,A),happ(s(fun(B,fun(C,A)),happ(s(fun(A,fun(B,fun(C,A))),V__1),s(A,X))),s(B,Y))) = s(fun(C,A),happ(s(fun(A,fun(C,A)),V__2),s(A,X))) => ![V__0]: (![X]: s(fun('h4/type/pair/prod'(B,C),A),happ(s(fun(A,fun('h4/type/pair/prod'(B,C),A)),V__0),s(A,X))) = s(fun('h4/type/pair/prod'(B,C),A),'h4/const/pair/UNCURRY'(s(fun(B,fun(C,A)),happ(s(fun(A,fun(B,fun(C,A))),V__1),s(A,X))))) => ![Funs]: s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,'h4/type/pair/prod'(B,C)),A),'h4/const/pair/UNCURRY'(s(fun(A,fun('h4/type/pair/prod'(B,C),A)),V__0))),s('h4/type/list/list'('h4/type/pair/prod'(A,'h4/type/pair/prod'(B,C))),Funs))) = s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,'h4/type/pair/prod'(B,C)),A),'h4/const/pair/FST'),s('h4/type/list/list'('h4/type/pair/prod'(A,'h4/type/pair/prod'(B,C))),Funs))))))).
