Commit 6f629be0 by Ralf Jung

### move quantifiers

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