the is_structure is a bad idea if you don't have canonical structures.

[helm.git] / helm / software / matita / dama / divisible_group.ma

diff --git a/helm/software/matita/dama/divisible_group.ma b/helm/software/matita/dama/divisible_group.ma
index 7d2eeed454871b3b273036d137561e511b216544..44db35a15ca0dfbef614568c71daeac17607f3d0 100644 (file)
--- a/helm/software/matita/dama/divisible_group.ma
+++ b/helm/software/matita/dama/divisible_group.ma
@@ -41,7 +41,7 @@ intro G; cases G; unfold divide; intros (x n); simplify;
 cases (f x n); simplify; exact H;
 qed.  
   
-lemma feq_pow: ∀G:dgroup.∀x,y:G.∀n.x≈y → n * x ≈ n * y.
+lemma feq_mul: ∀G:dgroup.∀x,y:G.∀n.x≈y → n * x ≈ n * y.
 intros (G x y n H); elim n; [apply eq_reflexive]
 simplify; apply (Eq≈ (x + (n1 * y)) H1);
 apply (Eq≈ (y+n1*y) H (eq_reflexive ??));
@@ -54,7 +54,7 @@ apply (ap_rewl ???? (plus_comm ???));
 apply (ap_rewl ???w (zero_neutral ??)); assumption;
 qed.
 
-lemma appow_ap: ∀G:dgroup.∀x,y:G.∀n.S n * x # S n * y → x # y.
+lemma apmul_ap: ∀G:dgroup.∀x,y:G.∀n.S n * x # S n * y → x # y.
 intros 4 (G x y n); elim n; [2:
   simplify in a;
   cases (applus ????? a); [assumption]
@@ -62,7 +62,7 @@ intros 4 (G x y n); elim n; [2:
 apply (plus_cancr_ap ??? 0); assumption;
 qed.
 
-lemma pluspow: ∀G:dgroup.∀x,y:G.∀n.n * (x+y) ≈ n * x + n * y.
+lemma plusmul: ∀G:dgroup.∀x,y:G.∀n.n * (x+y) ≈ n * x + n * y.
 intros (G x y n); elim n; [
   simplify; apply (Eq≈ 0 ? (zero_neutral ? 0)); apply eq_reflexive]
 simplify; apply eq_sym; apply (Eq≈ (x+y+(n1*x+n1*y))); [
@@ -78,7 +78,7 @@ simplify; apply eq_sym; apply (Eq≈ (x+y+(n1*x+n1*y))); [
 apply feq_plusl; apply eq_sym; assumption;
 qed. 
 
-lemma powzero: ∀G:dgroup.∀n.n*0 ≈ 0. [2: apply dg_carr; apply G]
+lemma mulzero: ∀G:dgroup.∀n.n*0 ≈ 0. [2: apply dg_carr; apply G]
 intros; elim n; [simplify; apply eq_reflexive]
 simplify; apply (Eq≈ ? (zero_neutral ??)); assumption; 
 qed.