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Diffstat (limited to 'Nicod1_4.v')
| -rw-r--r-- | Nicod1_4.v | 19 |
1 files changed, 19 insertions, 0 deletions
diff --git a/Nicod1_4.v b/Nicod1_4.v new file mode 100644 index 0000000..d32a096 --- /dev/null +++ b/Nicod1_4.v @@ -0,0 +1,19 @@ +Theorem N1_4 : ∀ P Q : Prop,
+ P ∨ Q → Q ∨ P.
+Proof. intros P Q.
+ specialize n2_2 with Q P.
+ intros n2_2a.
+ specialize Assoc1_5 with P Q P.
+ intros Assoc1_5a.
+ specialize Sum1_6 with P Q (Q ∨ P).
+ intros Sum1_6a.
+ MP Sum1_6a n2_2a.
+ Syll Sum1_6a Assoc1_5a Sa.
+ specialize Taut1_2 with P.
+ intros Taut1_2a.
+ specialize Sum1_6 with Q (P ∨ P) P.
+ intros Sum1_6b.
+ MP Sum1_6b Taut1_2a.
+ Syll Sa Sum1_6b Sb.
+ apply Sb.
+Qed.
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