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Diffstat (limited to 'theories/Init/Specif.v')
| -rw-r--r-- | theories/Init/Specif.v | 11 |
1 files changed, 11 insertions, 0 deletions
diff --git a/theories/Init/Specif.v b/theories/Init/Specif.v index 2cc2ecbc2..43a441fc5 100644 --- a/theories/Init/Specif.v +++ b/theories/Init/Specif.v @@ -207,6 +207,17 @@ Definition sig2_eta {A P Q} (p : { a : A | P a & Q a }) : p = exist2 _ _ (proj1_sig (sig_of_sig2 p)) (proj2_sig (sig_of_sig2 p)) (proj3_sig p). Proof. destruct p; reflexivity. Defined. +(** [exists x : A, B] is equivalent to [inhabited {x : A | B}] *) +Lemma exists_to_inhabited_sig {A P} : (exists x : A, P x) -> inhabited {x : A | P x}. +Proof. + intros [x y]. exact (inhabits (exist _ x y)). +Qed. + +Lemma inhabited_sig_to_exists {A P} : inhabited {x : A | P x} -> exists x : A, P x. +Proof. + intros [[x y]];exists x;exact y. +Qed. + (** [sumbool] is a boolean type equipped with the justification of their value *) |