diff options
| -rw-r--r-- | Makefile | 3 | ||||
| -rw-r--r-- | TODO | 3 | ||||
| -rw-r--r-- | theories/Logic/JMeq.v | 37 |
3 files changed, 42 insertions, 1 deletions
@@ -340,7 +340,8 @@ clean:: LOGICVO=theories/Logic/Classical.vo theories/Logic/Classical_Type.vo \ theories/Logic/Classical_Pred_Set.vo theories/Logic/Eqdep.vo \ theories/Logic/Classical_Pred_Type.vo theories/Logic/Classical_Prop.vo \ - theories/Logic/Eqdep_dec.vo theories/Logic/Decidable.vo + theories/Logic/Eqdep_dec.vo theories/Logic/Decidable.vo \ + theories/Logic/JMeq.v ARITHVO=theories/Arith/Arith.vo theories/Arith/Gt.vo \ theories/Arith/Between.vo theories/Arith/Le.vo \ @@ -45,3 +45,6 @@ Doc: + Set Printing Coercions +- Suggestions de la formation + Dans le Intros pattern on pourrait interpreter les _ +comme des hypotheses sur lesquelles on ferait Clear immediatement diff --git a/theories/Logic/JMeq.v b/theories/Logic/JMeq.v new file mode 100644 index 0000000000..2f8eda34f5 --- /dev/null +++ b/theories/Logic/JMeq.v @@ -0,0 +1,37 @@ +(*s John Major's Equality - C. Mc Bride *) + +Set Implicit Arguments. + +Inductive JMeq [A:Set;x:A] : (B:Set)B->Prop := + JMeq_refl : (JMeq x x). + +Hints Resolve JMeq_refl. + +Lemma JMeq_sym : (A,B:Set)(x:A)(y:B)(JMeq x y)->(JMeq y x). +Destruct 1; Trivial. +Save. + +Hints Immediate JMeq_sym. + +Lemma JMeq_trans : (A,B,C:Set)(x:A)(y:B)(z:C) + (JMeq x y)->(JMeq y z)->(JMeq x z). +Destruct 1; Trivial. +Save. + +Axiom JMeq_eq : (A:Set)(x,y:A)(JMeq x y)->(x=y). + +Lemma JMeq_eq_ind : (A:Set)(x,y:A)(P:A->Prop)(P x)->(JMeq x y)->(P y). +Intros A x y P H H'; Case JMeq_eq with 1:=H'; Trivial. +Save. + +Lemma JMeq_eq_rec : (A:Set)(x,y:A)(P:A->Set)(P x)->(JMeq x y)->(P y). +Intros A x y P H H'; Case JMeq_eq with 1:=H'; Trivial. +Save. + +Lemma JMeq_eq_ind_r : (A:Set)(x,y:A)(P:A->Prop)(P y)->(JMeq x y)->(P x). +Intros A x y P H H'; Case JMeq_eq with 1:=(JMeq_sym H'); Trivial. +Save. + +Lemma JMeq_eq_rec_r : (A:Set)(x,y:A)(P:A->Set)(P y)->(JMeq x y)->(P x). +Intros A x y P H H'; Case JMeq_eq with 1:=(JMeq_sym H'); Trivial. +Save. |
