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(exponentiation_aux
(expt_lower_bound 0
(expt_lower_bound-1 nil 3429504771
("" (induct "n")
(("1" (expand "expt") (("1" (propax) nil nil)) nil)
("2" (skosimp*)
(("2" (expand "expt" 1)
(("2" (inst - "px!1")
(("2"
(lemma "both_sides_times_pos_le1"
("pz" "px!1" "x" "1" "y" "expt(1+px!1,j!1)"))
(("2" (rewrite "expt_gt1_bound1" -1) (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(expt_gt1_bound1 formula-decl nil exponentiation nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types
nil)
(real_le_is_total_order name-judgement "(total_order?[real])" real_props
nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(posreal_expt application-judgement "posreal" exponentiation nil)
(nat_induction formula-decl nil naturalnumbers nil)
(expt def-decl "real" exponentiation nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(<= const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal" real_types
nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal" real_types
nil))
shostak)))