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Proof step 12 from proof exists-shiftw (previous step)

∀ a. ((Pa(a) -* P))(H) ⊦ ((_∃ Pa -* P))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 14:
∀ a. ((Pa(a) -* P))(H) ⊦ ∀ H1. H1 ⊥ H ∧ (_∃ Pa)(H1) → P(H1 ∪ H)

Rule argument

spec: heap-sep name: wand seq: ⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H)) subst: [H, P1, P0] → [H, P, _∃ Pa] flags: <all paths>

Additional information

Used terms: H, P, _∃ Pa