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Diffstat (limited to 'contrib/funind/Recdef.v')
-rw-r--r-- | contrib/funind/Recdef.v | 48 |
1 files changed, 0 insertions, 48 deletions
diff --git a/contrib/funind/Recdef.v b/contrib/funind/Recdef.v deleted file mode 100644 index 2d206220..00000000 --- a/contrib/funind/Recdef.v +++ /dev/null @@ -1,48 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) -Require Compare_dec. -Require Wf_nat. - -Section Iter. -Variable A : Type. - -Fixpoint iter (n : nat) : (A -> A) -> A -> A := - fun (fl : A -> A) (def : A) => - match n with - | O => def - | S m => fl (iter m fl def) - end. -End Iter. - -Theorem SSplus_lt : forall p p' : nat, p < S (S (p + p')). - intro p; intro p'; change (S p <= S (S (p + p'))); - apply le_S; apply Gt.gt_le_S; change (p < S (p + p')); - apply Lt.le_lt_n_Sm; apply Plus.le_plus_l. -Qed. - - -Theorem Splus_lt : forall p p' : nat, p' < S (p + p'). - intro p; intro p'; change (S p' <= S (p + p')); - apply Gt.gt_le_S; change (p' < S (p + p')); apply Lt.le_lt_n_Sm; - apply Plus.le_plus_r. -Qed. - -Theorem le_lt_SS : forall x y, x <= y -> x < S (S y). -intro x; intro y; intro H; change (S x <= S (S y)); - apply le_S; apply Gt.gt_le_S; change (x < S y); - apply Lt.le_lt_n_Sm; exact H. -Qed. - -Inductive max_type (m n:nat) : Set := - cmt : forall v, m <= v -> n <= v -> max_type m n. - -Definition max : forall m n:nat, max_type m n. -intros m n; case (Compare_dec.le_gt_dec m n). -intros h; exists n; [exact h | apply le_n]. -intros h; exists m; [apply le_n | apply Lt.lt_le_weak; exact h]. -Defined. |