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Proof step 34 from proof introduce-sharing (previous step)

((P -* P1))(H2), P(H), H2 ⊥ H, H1 ⊥ H2, H1 ⊥ H, ∀ H0. H0 ⊥ H1 ∧ P(H0) → P0(H0 ∪ H1) ⊦ ∃ H0, H3, H4. H0 ⊥ H4 ∧ H0 ⊥ H3 ∧ H3 ⊥ H4 ∧ H1 ∪ H2 ∪ H = H0 ∪ H3 ∪ H4 ∧ P0(H0 ∪ H4) ∧ P1(H3 ∪ H4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 36:
P(H), H1 ⊥ H, H1 ⊥ H2, H2 ⊥ H, ∀ H0. H0 ⊥ H1 ∧ P(H0) → P0(H0 ∪ H1), ∀ H1. H1 ⊥ H2 ∧ P(H1) → P1(H1 ∪ H2) ⊦ ∃ H0, H3, H4. H0 ⊥ H4 ∧ H0 ⊥ H3 ∧ H3 ⊥ H4 ∧ H1 ∪ H2 ∪ H = H0 ∪ H3 ∪ H4 ∧ P0(H0 ∪ H4) ∧ P1(H3 ∪ H4)

Rule argument

spec: <toplevel> name: wand seq: ⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H)) subst: [H, P1, P0] → [H2, P1, P] flags: <all paths>

Additional information

Used terms: H2, P1, P