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Proof step 51 from proof propagate (previous step)

!(me, O2, P)(H0), P0(H), rely(me, O1, H0 ∪ H, O2, H2), H0 ⊥ H ⊦ id = me, (r ∈ H0 → r ∈ H2) ∧ (r ∈ H0 → H0[r] = H2[r])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ rely(me, O1, H1, O2, H2) ↔ (∀ r. (O1(r) = me ↔ O2(r) = me) ∧ (O1(r) = me → (r ∈ H1 ↔ r ∈ H2) ∧ (r ∈ H1 → H1[r] = H2[r])))
Proof step 53:
!(me, O2, P)(H0), P0(H), H0 ⊥ H, ∀ r. (O1(r) = me ↔ O2(r) = me) ∧ (O1(r) = me → (r ∈ H0 ∪ H ↔ r ∈ H2) ∧ (r ∈ H0 ∪ H → (H0 ∪ H)[r] = H2[r])) ⊦ id = me, (r ∈ H0 → r ∈ H2) ∧ (r ∈ H0 → H0[r] = H2[r])

Rule argument

spec: <toplevel> name: rely seq: ⊦ rely(me, O1, H1, O2, H2) ↔ (∀ r. (O1(r) = me ↔ O2(r) = me) ∧ ( O1(r) = me → (r ∈ H1 ↔ r ∈ H2) ∧ (r ∈ H1 → H1[r] = H2[r]))) subst: [H2, O2, H1, O1, me] → [H2, O2, H0 ∪ H, O1, me] flags: <all paths>

Additional information

Used terms: H2, O2, H0 ∪ H, O1, me