diff --git a/theories/nat_cancel.v b/theories/nat_cancel.v index 97f5437623839f71e2470a061611ea98f0101797..6202dacc96132db780c0a8ebe98ea92e057030a7 100644 --- a/theories/nat_cancel.v +++ b/theories/nat_cancel.v @@ -1,6 +1,6 @@ From stdpp Require Import numbers. -(* The class [NatCancel m n m' n'] is a simple canceler for natural numbers +(** The class [NatCancel m n m' n'] is a simple canceler for natural numbers implemented using type classes. Input: [m], [n]; output: [m'], [n']. @@ -71,7 +71,7 @@ Global Instance nat_cancel_leaf_S_else m n m' n' : NatCancelLeaf m n m' n' → NatCancelLeaf m (S n) m' (S n') | 4. Proof. unfold NatCancelLeaf, NatCancel. omega. Qed. -(* The instance [nat_cancel_S_both] is redundant, but may reduce proof search +(** The instance [nat_cancel_S_both] is redundant, but may reduce proof search quite a bit, e.g. when canceling constants in constants. *) Global Instance nat_cancel_S_both m n m' n' : NatCancel m n m' n' → NatCancel (S m) (S n) m' n' | 1. @@ -83,4 +83,4 @@ Proof. unfold NatCancel, MakeNatPlus. omega. Qed. Global Instance nat_cancel_S m m' m'' Sm' n n' n'' : NatCancel m n m' n' → NatCancelLeaf 1 n' m'' n'' → MakeNatS m'' m' Sm' → NatCancel (S m) n Sm' n'' | 3. -Proof. unfold NatCancelLeaf, NatCancel, MakeNatS. omega. Qed. \ No newline at end of file +Proof. unfold NatCancelLeaf, NatCancel, MakeNatS. omega. Qed.