%   ORIGINAL: h4/integer__word/WORD__LEi
% 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
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/integer/INT__LE__LT: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm: h4/words/WORD__LESS__OR__EQ: !b a. h4/words/word__le a b <=> h4/words/word__lt a b \/ a = b
% Assm: h4/integer__word/w2i__11: !w v. h4/integer__word/w2i v = h4/integer__word/w2i w <=> v = w
% Assm: h4/integer__word/WORD__LTi: !b a. h4/words/word__lt a b <=> h4/integer/int__lt (h4/integer__word/w2i a) (h4/integer__word/w2i b)
% Goal: !b a. h4/words/word__le a b <=> h4/integer/int__le (h4/integer__word/w2i a) (h4/integer__word/w2i b)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_integers_INTu_u_LEu_u_LT]: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm [h4s_wordss_WORDu_u_LESSu_u_ORu_u_EQ]: !b a. h4/words/word__le a b <=> h4/words/word__lt a b \/ a = b
% Assm [h4s_integeru_u_words_w2iu_u_11]: !w v. h4/integer__word/w2i v = h4/integer__word/w2i w <=> v = w
% Assm [h4s_integeru_u_words_WORDu_u_LTi]: !b a. h4/words/word__lt a b <=> h4/integer/int__lt (h4/integer__word/w2i a) (h4/integer__word/w2i b)
% Goal: !b a. h4/words/word__le a b <=> h4/integer/int__le (h4/integer__word/w2i a) (h4/integer__word/w2i b)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q297656,TV_Q297652]: ![V_f, V_g]: (![V_x]: s(TV_Q297652,happ(s(t_fun(TV_Q297656,TV_Q297652),V_f),s(TV_Q297656,V_x))) = s(TV_Q297652,happ(s(t_fun(TV_Q297656,TV_Q297652),V_g),s(TV_Q297656,V_x))) => s(t_fun(TV_Q297656,TV_Q297652),V_f) = s(t_fun(TV_Q297656,TV_Q297652),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_integers_INTu_u_LEu_u_LT, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) | s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y)))).
fof(ah4s_wordss_WORDu_u_LESSu_u_ORu_u_EQ, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) <=> (p(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) | s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))).
fof(ah4s_integeru_u_words_w2iu_u_11, axiom, ![TV_u_27a]: ![V_w, V_v]: (s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))) = s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))).
fof(ah4s_integeru_u_words_WORDu_u_LTi, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ch4s_integeru_u_words_WORDu_u_LEi, conjecture, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
