V_______________________________________________________________ *)
include "arithmetics/div_and_mod.ma".
+include "basics/core_notation/exp_2.ma".
let rec exp n m on m ≝
match m with
-
\ No newline at end of file
+
V_______________________________________________________________ *)
include "arithmetics/nat.ma".
+include "basics/core_notation/exp_2.ma".
(* iteration *)
g^i a ≤ g^j a.
#g #a #i #j #leg #leij elim leij //
#m #leim #Hind normalize @(transitive_le … Hind) @leg
-qed.
\ No newline at end of file
+qed.
(* other notations **********************************************************)
-notation < "term 76 a \sup term 90 b" non associative with precedence 75 for @{ 'exp $a $b}.
-notation > "a \sup term 90 b" non associative with precedence 75 for @{ 'exp $a $b}.
-notation > "a ^ term 90 b" non associative with precedence 75 for @{ 'exp $a $b}.
-notation "s \sup (-1)" non associative with precedence 75 for @{ 'invert $s }.
-notation > "s ^ (-1)" non associative with precedence 75 for @{ 'invert $s }.
-notation < "s \sup (-1) x" non associative with precedence 90 for @{ 'invert_appl $s $x}.
-
notation "| term 19 C |" with precedence 70 for @{ 'card $C }.
notation "\naturals" non associative with precedence 90 for @{'N}.
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+(* Core notation *******************************************************)
+
+notation < "term 76 a \sup term 90 b" non associative with precedence 75 for @{ 'exp $a $b}.
+notation > "a \sup term 90 b" non associative with precedence 75 for @{ 'exp $a $b}.
+notation > "a ^ term 90 b" non associative with precedence 75 for @{ 'exp $a $b}.
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+(* Core notation *******************************************************)
+
+notation "s \sup (-1)" non associative with precedence 75 for @{ 'invert $s }.
+notation > "s ^ (-1)" non associative with precedence 75 for @{ 'invert $s }.
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+(* Core notation *******************************************************)
+
+notation < "s \sup (-1) x" non associative with precedence 90 for @{ 'invert_appl $s $x}.
include "formal_topology/cprop_connectives.ma".
include "basics/core_notation/compose_2.ma".
+include "basics/core_notation/invert_1.ma".
inductive eq (A:Type[0]) (x:A) : A → CProp[0] ≝
refl: eq A x x.
include "reverse_complexity/bigops_compl.ma".
+include "basics/core_notation/napart_2.ma".
(********************************* the speedup ********************************)
@Hmono @(mono_h_of2 … Hr Hmono … ltin)
]
qed.
-
\ No newline at end of file
+
include "basics/types.ma".
include "arithmetics/nat.ma".
include "hints_declaration.ma".
+include "basics/core_notation/invert_1.ma".
(******************* Quotienting in type theory **********************)