28 lines
499 B
Coq
28 lines
499 B
Coq
|
From Coq Require Import Arith List.
|
||
|
|
From Coq Require Import Lia.
|
||
|
|
Require Import Ring.
|
||
|
|
|
||
|
|
Theorem plus_id_exercise : forall n m o : nat,
|
||
|
|
n = m -> m = o -> n + m = m + o.
|
||
|
|
Proof.
|
||
|
|
lia.
|
||
|
|
Qed.
|
||
|
|
|
||
|
|
Theorem add_assoc : forall n m p : nat,
|
||
|
|
n + (m + p) = (n + m) + p.
|
||
|
|
Proof.
|
||
|
|
lia.
|
||
|
|
Qed.
|
||
|
|
|
||
|
|
Theorem S_injective : forall (n m : nat),
|
||
|
|
S n = S m -> n = m.
|
||
|
|
Proof.
|
||
|
|
congruence.
|
||
|
|
Qed.
|
||
|
|
|
||
|
|
Theorem or_distributes_over_and : forall P Q R : Prop,
|
||
|
|
P \/ (Q /\ R) <-> (P \/ Q) /\ (P \/ R).
|
||
|
|
Proof.
|
||
|
|
intuition.
|
||
|
|
Qed.
|