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Proof step 6 from proof exists-shiftw (previous step)

∀ H0. H0 ⊥ H ∧ (∃ a. Pa(a)(H0)) → P(H0 ∪ H) ⊦ ((Pa(a) -* P))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 8:
∀ H0. H0 ⊥ H ∧ (∃ a. Pa(a)(H0)) → P(H0 ∪ H) ⊦ ∀ H1. H1 ⊥ H ∧ Pa(a)(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(a)] flags: <all paths>

Additional information

Used terms: H, P, Pa(a)