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Proof step 73 from proof alloc-p (previous step)

H1 ++ r = H0 ∪ H4 ∪ H3, (H1 ++ r)[r] = H2[r], !(O2(r), O2, P)(H4), !(O2(r), O2, r =>_)(H0), r =>_(H0), P(H4), P0(H3), r ∈ H4, r ∈ H2, H0 ⊥ H3, H4 ⊥ H3, ∀ r0. ((r = r0 ⊃ O2(r0);O1(r0)) = O2(r) ↔ O2(r0) = O2(r)) ∧ ((r = r0 ⊃ O2(r0);O1(r0)) = O2(r) → (r0 = r ∨ r0 ∈ H1 ↔ r0 ∈ H2) ∧ (r0 ∈ H1 → (H1 ++ r)[r0] = H2[r0])), ∀ r. ¬ r ∈ H0 ∨ ¬ r ∈ H4 ⊦ O1(r) = O2(r), ((!(O2(r), O1, P) * P0))(H4 ∪ H3), ((!(O2(r), O1, P) * P0))(H1), r ∈ H1, r ∈ H0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: maplet name: mapex seq: ⊦ r =>_ = _∃(λ o. r => o) subst: [r] → [r] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (_∃ oP)(H) ↔ (∃ o. oP(o)(H)); (s)% ⊦ ((r => o))(H) → r ∈ H; (s) Used terms: r