Let iAssumption succeed when there is H : False.

theories/proofmode/class_instances.v

@@ -10,6 +10,8 @@ Context {M : ucmraT}.
 Implicit Types P Q R : uPred M.
 
 (* FromAssumption *)
+Global Instance from_assumption_False p P : FromAssumption p False P.
+Proof. destruct p; rewrite /FromAssumption /= ?always_pure; apply False_elim. Qed.
 Global Instance from_assumption_exact p P : FromAssumption p P P.
 Proof. destruct p; by rewrite /FromAssumption /= ?always_elim. Qed.
 Global Instance from_assumption_always_l p P Q :

theories/tests/proofmode.v

@@ -127,3 +127,6 @@ Proof. iIntros "HP". iExists (0:nat). iApply ("HP" $! (0:nat)). Qed.
 
 Lemma demo_13 (M : ucmraT) (P : uPred M) : (|==> False) -∗ |==> P.
 Proof. iIntros. iAssert False%I with ">[-]" as "[]". done. Qed.
+
+Lemma demo_14 (M : ucmraT) (P : uPred M) : False -∗ P.
+Proof. iIntros "H". done. Qed.