matita/matita/contribs/RELATIONAL/NLE/inv.ma

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   3 (*      ||M||                                                             *)
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  14
  15
  16
  17 include "NLE/defs.ma".
  18
  19 theorem nle_inv_succ_1: ∀x,y. x < y →
  20                         ∃z. y = succ z ∧ x ≤ z.
  21  intros; inversion H; clear H; intros; destruct. autobatch.
  22 qed.
  23
  24 theorem nle_inv_succ_succ: ∀x,y. x < succ y → x ≤ y.
  25  intros; inversion H; clear H; intros; destruct. autobatch.
  26 qed.
  27
  28 theorem nle_inv_succ_zero: ∀x. x < zero → False.
  29  intros. inversion H; clear H; intros; destruct.
  30 qed.
  31
  32 theorem nle_inv_zero_2: ∀x. x ≤ zero → x = zero.
  33  intros; inversion H; clear H; intros; destruct. autobatch.
  34 qed.
  35
  36 theorem nle_inv_succ_2: ∀y,x. x ≤ succ y →
  37                         x = zero ∨ ∃z. x = succ z ∧ z ≤ y.
  38  intros; inversion H; clear H; intros; destruct;
  39  autobatch depth = 4.
  40 qed.