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minimal changes to documentation to test coq2html (#1108)
* test a few files
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classical/boolp.v

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@@ -7,18 +7,18 @@
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From HB Require Import structures.
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From mathcomp Require Import all_ssreflect.
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(******************************************************************************)
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(* Classical Logic *)
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(***md*************************************************************************)
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(* # Classical Logic *)
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(* *)
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(* This file provides the axioms of classical logic and tools to perform *)
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(* classical reasoning in the Mathematical Compnent framework. The three *)
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(* axioms are taken from the standard library of Coq, more details can be *)
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(* found in Section 5 of *)
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(* Reynald Affeldt, Cyril Cohen, Damien Rouhling: *)
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(* Formalization Techniques for Asymptotic Reasoning in Classical Analysis. *)
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(* Journal of Formalized Reasoning, 2018 *)
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(* - R. Affeldt, C. Cohen, D. Rouhling. Formalization Techniques for *)
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(* Asymptotic Reasoning in Classical Analysis. JFR 2018 *)
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(* *)
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(* * Axioms *)
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(* ## Axioms *)
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(* ``` *)
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(* functional_extensionality_dep == functional extensionality (on dependently *)
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(* typed functions), i.e., functions that are pointwise *)
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(* equal are equal *)
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(* constructive_indefinite_description == existential in Prop (ex) implies *)
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(* existential in Type (sig) *)
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(* cid := constructive_indefinite_description (shortcut) *)
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(* --> A number of properties are derived below from these axioms and are *)
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(* ``` *)
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(* *)
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(* A number of properties are derived below from these axioms and are *)
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(* often more pratical to use than directly using the axioms. For instance *)
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(* propext, funext, the excluded middle (EM),... *)
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(* *)
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(* * Boolean View of Prop *)
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(* ## Boolean View of Prop *)
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(* ``` *)
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(* `[< P >] == boolean view of P : Prop, see all lemmas about asbool *)
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(* ``` *)
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(* *)
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(* * Mathematical Components Structures *)
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(* ## Mathematical Components Structures *)
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(* ``` *)
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(* {classic T} == Endow T : Type with a canonical eqType/choiceType. *)
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(* This is intended for local use. *)
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(* E.g., T : Type |- A : {fset {classic T}} *)
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(* {eclassic T} == Endow T : eqType with a canonical choiceType. *)
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(* On the model of {classic _}. *)
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(* See also the lemmas Peq and eqPchoice. *)
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(* ``` *)
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(* *)
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(* --> Functions into a porderType (resp. latticeType) are equipped with *)
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(* Functions into a porderType (resp. latticeType) are equipped with *)
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(* a porderType (resp. latticeType), (f <= g)%O when f x <= g x for all x, *)
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(* see lemma lefP. *)
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(******************************************************************************)

classical/cardinality.v

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@@ -3,8 +3,8 @@ From HB Require Import structures.
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From mathcomp Require Import all_ssreflect finmap ssralg ssrnum ssrint rat.
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From mathcomp Require Import mathcomp_extra boolp classical_sets functions.
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(******************************************************************************)
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(* Cardinality *)
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(***md*************************************************************************)
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(* # Cardinality *)
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(* *)
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(* This file provides an account of cardinality properties of classical sets. *)
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(* This includes standard results of set theory such as the Pigeon Hole *)
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(* only relations A #<= B and A #= B to compare the cardinals of two sets *)
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(* (on two possibly different types). *)
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(* *)
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(* ``` *)
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(* A #<= B == the cardinal of A is smaller or equal to the one of B *)
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(* A #>= B := B #<= A *)
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(* A #= B == the cardinal of A is equal to the cardinal of B *)
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(* A.`1 := [fset x.1 | x in A] *)
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(* A.`2 := [fset x.2 | x in A] *)
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(* {fimfun aT >-> T} == type of functions with a finite image *)
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(* ``` *)
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(* *)
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(******************************************************************************)
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