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Coq generates different induction schemes depending on whether a data type inhabits Prop or not:
Inductive evenA : nat -> Type :=
evenA0 : evenA 0
| evenASS : forall n, evenA n -> evenA (S (S n)).
Inductive evenB : nat -> Prop :=
evenB0 : evenB 0
| evenBSS : forall n, evenB n -> evenB (S (S n)).
Check evenA_ind.
(*evenA_ind : forall P : forall n : nat, evenA n -> Prop, P 0 evenA0 -> (forall (n : nat) (e : evenA n), P n e -> P (S (S n)) (evenASS n e)) -> forall (n : nat) (e : evenA n), P n e*)Check evenB_ind.
(*evenB_ind : forall P : nat -> Prop, P 0 -> (forall n : nat, evenB n -> P n -> P (S (S n))) -> forall n : nat, evenB n -> P n*)
eliminators should permit the generation of induction schemes à laevenB_ind. (What should we call these?)
The text was updated successfully, but these errors were encountered:
Coq generates different induction schemes depending on whether a data type inhabits
Prop
or not:eliminators
should permit the generation of induction schemes à laevenB_ind
. (What should we call these?)The text was updated successfully, but these errors were encountered: