unfold not. intros. apply H. symmetry. assumption.
qed.
-theorem trans_eq : ∀A:Type.∀x,y,z:A.x=y→y=z→x=z.
- intros;
- transitivity y;
- assumption.
+theorem trans_eq : \forall A:Type. \forall x,y,z:A. x=y \to y=z \to x=z.
+ intros. transitivity y; assumption.
qed.
-theorem plus_reg_l: \forall (n,m,p:nat). n + m = n + p \to m = p.
+theorem plus_reg_l: \forall n,m,p. n + m = n + p \to m = p.
intros. apply plus_reg_l; auto.
qed.
<keyword>normalize</keyword>
<keyword>reduce</keyword>
<keyword>reflexivity</keyword>
- <keyword>rename</keyword>
<keyword>replace</keyword>
<keyword>rewrite</keyword>
<keyword>ring</keyword>