| ⊢ | w ≡ w | DiState |
Proof for ⊃ :
1 | ⊢ ¬w ⊃¬w | |
2 | ⊢ ¬w ⊃¬¬¬w | 1, def. of |
3 | ⊢ (¬w ⊃ ¬¬¬w) ⊃ ( ¬¬w ⊃ w) | |
4 | ⊢ ¬¬w ⊃ w | |
5 | ⊢ w ⊃¬¬w | |
6 | ⊢ w ⊃¬¬w | |
7 | ⊢ w ⊃ w |
qed
Proof for ⊂:
1 | w ⊃ w | |
qed
Here are two important corollaries of DiState that are easy to prove: