task41.v

Ltac split_all := repeat try split.

(* 以下は動作確認用 *)

Lemma bar :
  forall P Q R S : Prop,
    R -> Q -> P -> S -> (P /\ R) /\ (S /\ Q).
Proof.
  intros P Q R S H0 H1 H2 H3.
  split_all.
  - assumption.
  - assumption.
  - assumption.
  - assumption.
Qed.

Lemma baz :
  forall P Q R S T : Prop,
    R -> Q -> P -> T -> S -> P /\ Q /\ R /\ S /\ T.
Proof.
  intros P Q R S T H0 H1 H2 H3 H4.
  split_all.
  - assumption.
  - assumption.
  - assumption.
  - assumption.
  - assumption.
Qed.

Lemma quux :
  forall P Q : Type, P -> Q -> P * Q.
Proof.
  intros P Q H0 H1.
  split_all.
  - assumption.
  - assumption.
Qed.

Record foo := {
  x : (False -> False) /\ True /\ (False -> False);
  y : True;
  z : (False -> False) /\ True
}.

Lemma hogera : foo.
Proof.
  split_all.
  - intros H; exact H.
  - intros H; exact H.
  - intros H; exact H.
Qed.

task42.v

Require Import Arith.
Require Import Omega.
Require Import Recdef.

Function log(n:nat) {wf lt n} :=
  if le_lt_dec n 1 then
    0
  else
    S (log (Div2.div2 n)).
Proof.
  intros.
  apply Div2.lt_div2.
  omega.
  apply lt_wf.
Qed.

task43.v

Ltac split_all := 
  match goal with
  | |- (_ /\ _) => try split;split_all
  | |- _ => idtac
  end.

(* 以下は動作確認用 *)

Lemma bar :
  forall P Q R S : Prop,
    R -> Q -> P -> S -> (P /\ R) /\ (S /\ Q).
Proof.
  intros P Q R S H0 H1 H2 H3.
  split_all.
  - assumption.
  - assumption.
  - assumption.
  - assumption.
Qed.

Lemma baz :
  forall P Q R S T : Prop,
    R -> Q -> P -> T -> S -> P /\ Q /\ R /\ S /\ T.
Proof.
  intros P Q R S T H0 H1 H2 H3 H4.
  split_all.
  - assumption.
  - assumption.
  - assumption.
  - assumption.
  - assumption.
Qed.

Lemma quux :
  forall P Q : Type, P -> Q -> P * Q.
Proof.
  intros P Q H0 H1.
  split_all.
  split.
  - assumption.
  - assumption.
Qed.