%   ORIGINAL: 'h4/thm/integral/INTEGRABLE_SUBINTERVAL_'
% 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: !f a b c d. 'h4/const/real/real_lte' a c /\ 'h4/const/real/real_lte' c d /\ 'h4/const/real/real_lte' d b /\ 'h4/const/integral/integrable' ('h4/const/pair/,' a b) f ==> 'h4/const/integral/integrable' ('h4/const/pair/,' c d) f
%   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: !f a b c d. 'h4/const/real/real_lte' a c /\ 'h4/const/real/real_lte' c d /\ 'h4/const/real/real_lte' d b /\ 'h4/const/integral/integrable' ('h4/const/pair/,' a b) f ==> 'h4/const/integral/integrable' ('h4/const/pair/,' c d) f
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_3f41134,V_3f41130]: ![F, G]: (![X]: s(V_3f41130,happ(s(fun(V_3f41134,V_3f41130),F),s(V_3f41134,X))) = s(V_3f41130,happ(s(fun(V_3f41134,V_3f41130),G),s(V_3f41134,X))) => s(fun(V_3f41134,V_3f41130),F) = s(fun(V_3f41134,V_3f41130),G))).
fof('h4/thm/integral/INTEGRABLE_SUBINTERVAL_', conjecture, ![F, A, B, C, D]: ((p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',A),s('h4/type/realax/real',C)))) & (p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',C),s('h4/type/realax/real',D)))) & (p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',D),s('h4/type/realax/real',B)))) & p(s(bool,'h4/const/integral/integrable'(s('h4/type/pair/prod'('h4/type/realax/real','h4/type/realax/real'),'h4/const/pair/,'(s('h4/type/realax/real',A),s('h4/type/realax/real',B))),s(fun('h4/type/realax/real','h4/type/realax/real'),F))))))) => p(s(bool,'h4/const/integral/integrable'(s('h4/type/pair/prod'('h4/type/realax/real','h4/type/realax/real'),'h4/const/pair/,'(s('h4/type/realax/real',C),s('h4/type/realax/real',D))),s(fun('h4/type/realax/real','h4/type/realax/real'),F)))))).
