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Proof step 10 from proof write-known-p (previous step)

((r => o0 * P))(H0), P0(H), rely(me, O1, (H0 ∪ H)[r, o1], O2, H2), H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ((!(me, O2, r => o1 * P) * P0))((H0 ∪ H)[r, o1])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ r ∈ H0 ∧ H0 ⊥ H1 → (H0 ∪ H1)[r, o] = H0[r, o] ∪ H1
Proof step 12:
((r => o0 * P))(H0), P0(H), rely(me, O1, H0[r, o1] ∪ H, O2, H2), r ∈ H0, H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ((!(me, O2, r => o1 * P) * P0))(H0[r, o1] ∪ H)

Rule argument

spec: heap name: write-left seq: ⊦ r ∈ H0 ∧ H0 ⊥ H1 → (H0 ∪ H1)[r, o] = H0[r, o] ∪ H1 subst: [o, r, H1, H0] → [o1, r, H, H0] flags: <all paths>

Additional information

Used simplifier rules: sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep% ⊦ ((r => o * P))(H) → r ∈ H; (s) Used terms: o1, r, H, H0