Commit 6f629be0 authored by Ralf Jung's avatar Ralf Jung

move quantifiers

parent 5ac2997a
......@@ -20,7 +20,7 @@ Section least.
Lemma F_fix_implies_least_fixpoint x : F (uPred_least_fixpoint F) x uPred_least_fixpoint F x.
Proof.
iIntros "HF" (P). iApply wand_impl_always. iIntros "#Hincl".
iIntros "HF" (P) "#Hincl".
iApply "Hincl". iApply (Hmono _ P); last done.
iIntros "!#" (y) "Hy". iApply "Hy". done.
Qed.
......@@ -39,9 +39,9 @@ Section least.
apply (anti_symm _); auto using least_fixpoint_implies_F_fix, F_fix_implies_least_fixpoint.
Qed.
Lemma uPred_least_fixpoint_ind (P : A uPred M) (x : A) :
( y, F P y - P y) - uPred_least_fixpoint F x - P x.
Proof. iIntros "#HP HF". iApply "HF". done. Qed.
Lemma uPred_least_fixpoint_ind (P : A uPred M) :
( y, F P y - P y) - x, uPred_least_fixpoint F x - P x.
Proof. iIntros "#HP" (x) "HF". iApply "HF". done. Qed.
End least.
Section greatest.
......@@ -70,7 +70,7 @@ Section greatest.
apply (anti_symm _); auto using greatest_fixpoint_implies_F_fix, F_fix_implies_greatest_fixpoint.
Qed.
Lemma uPred_greatest_fixpoint_coind (P : A uPred M) (x : A) :
( y, P y - F P y) - P x - uPred_greatest_fixpoint F x.
Proof. iIntros "#HP Hx". iExists P. by iIntros "{$Hx} !#". Qed.
Lemma uPred_greatest_fixpoint_coind (P : A uPred M) :
( y, P y - F P y) - x, P x - uPred_greatest_fixpoint F x.
Proof. iIntros "#HP" (x) "Hx". iExists P. by iIntros "{$Hx} !#". Qed.
End greatest.
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