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Proof step 48 from proof propagate (previous step)

!(me, O2, P)(H0), P0(H), rely(me, O1, H0 ∪ H, O2, H2), H0 ⊥ H ⊦ id = me, H0 ⊆ H2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ H0 ⊆ H1 ↔ (∀ r. (r ∈ H0 → r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 50:
!(me, O2, P)(H0), P0(H), rely(me, O1, H0 ∪ H, O2, H2), H0 ⊥ H ⊦ id = me, ∀ r. (r ∈ H0 → r ∈ H2) ∧ (r ∈ H0 → H0[r] = H2[r])

Rule argument

spec: heap name: subset seq: ⊦ H0 ⊆ H1 ↔ (∀ r. (r ∈ H0 → r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [H2, H0] flags: <all paths>

Additional information

Used terms: H2, H0