Library hw02_simple_tautologies


Require Import Classical_Prop.

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Also Check this URL: https://bit.ly/35ZsvXx Students did one tautology each depending on their student ID.

Warmup Exercise


Lemma DubNeg: forall b: Prop, b -> ~~b.
Proof.
Admitted.

Problems in H2.P5


Lemma Dec01: forall a: Prop, ~~(((a/\a)/\a)<->a).
Proof.
  Admitted.

Lemma Dec03: forall a b: Prop, ~~(((a/\b)/\b)-> b).
Proof.
  Admitted.

Lemma Dec04: forall a b c: Prop, ~ ~ (((a/\b)/\c) -> c).
Proof.
  Admitted.

Lemma Dec07: forall a b: Prop, ~~(((a\/b)/\a)->a).
Proof.
  Admitted.

Lemma Dec16: forall a b: Prop, ~~((a/\~~~~b)->a).
Proof.
  Admitted.

Lemma Dec17: forall a b: Prop, ~~((a/\(a/\b))->b).
Proof.
  Admitted.


Lemma Dec18: forall a b: Prop, ~~((a /\( a <-> b))->b).
Proof.
  Admitted.

Lemma Dec19: forall a : Prop, ~~((a/\(a->a))->a).
Proof.
  Admitted.

Lemma Dec20: forall a b: Prop, ~~((a/\(b\/a))<->a).
Proof.
  Admitted.

Lemma Dec21: forall a b: Prop, ~~((a/\(b<->a))->a).
Proof.
  Admitted.

Lemma Dec22: forall a b: Prop, ~~((a/\a)\/(b->b)).
Proof.
  Admitted.

Lemma Dec24: forall a b: Prop, ~~((a/\b)\/(a<->a)).
Proof.
  Admitted.