%   ORIGINAL: 'h4/thm/quotient/LET_RES_ABSTRACT_'
% 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: !r lam v. 'h4/const/bool/IN' v r ==> 'h4/const/bool/LET' ('h4/const/bool/RES_ABSTRACT' r lam) v = 'h4/const/bool/LET' lam v
%   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: !r lam v. 'h4/const/bool/IN' v r ==> 'h4/const/bool/LET' ('h4/const/bool/RES_ABSTRACT' r lam) v = 'h4/const/bool/LET' lam v
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_3f75290,V_3f75286]: ![F, G]: (![X]: s(V_3f75286,happ(s(fun(V_3f75290,V_3f75286),F),s(V_3f75290,X))) = s(V_3f75286,happ(s(fun(V_3f75290,V_3f75286),G),s(V_3f75290,X))) => s(fun(V_3f75290,V_3f75286),F) = s(fun(V_3f75290,V_3f75286),G))).
fof('h4/thm/quotient/LET_RES_ABSTRACT_', conjecture, ![B,A]: ![R, Lam, V]: (p(s(bool,'h4/const/bool/IN'(s(A,V),s(fun(A,bool),R)))) => s(B,'h4/const/bool/LET'(s(fun(A,B),'h4/const/bool/RES_ABSTRACT'(s(fun(A,bool),R),s(fun(A,B),Lam))),s(A,V))) = s(B,'h4/const/bool/LET'(s(fun(A,B),Lam),s(A,V))))).
