%   ORIGINAL: 'h4/thm/arithmetic/findq_divisor_'
% 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: !n m a. 'h4/const/arithmetic/<=' n m ==> 'h4/const/arithmetic/<=' ('h4/const/arithmetic/*' ('h4/const/arithmetic/findq' ('h4/const/pair/,' a ('h4/const/pair/,' m n))) n) ('h4/const/arithmetic/*' a 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: !n m a. 'h4/const/arithmetic/<=' n m ==> 'h4/const/arithmetic/<=' ('h4/const/arithmetic/*' ('h4/const/arithmetic/findq' ('h4/const/pair/,' a ('h4/const/pair/,' m n))) n) ('h4/const/arithmetic/*' a 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_3f85718,V_3f85714]: ![F, G]: (![X]: s(V_3f85714,happ(s(fun(V_3f85718,V_3f85714),F),s(V_3f85718,X))) = s(V_3f85714,happ(s(fun(V_3f85718,V_3f85714),G),s(V_3f85718,X))) => s(fun(V_3f85718,V_3f85714),F) = s(fun(V_3f85718,V_3f85714),G))).
fof('h4/thm/arithmetic/findq_divisor_', conjecture, ![N, M, A]: (p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',N),s('h4/type/num/num',M)))) => p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num','h4/const/arithmetic/findq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/pair/prod'('h4/type/num/num','h4/type/num/num')),'h4/const/pair/,'(s('h4/type/num/num',A),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/pair/,'(s('h4/type/num/num',M),s('h4/type/num/num',N))))))),s('h4/type/num/num',N))),s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num',A),s('h4/type/num/num',M)))))))).
