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Proof step 21 from proof modify-agree (previous step)

modify(rs)(H0, H), r ∈ rs, ((H ≡ H1))(rs) ⊦ # rs = 0, rs = ∅, (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ((H0 ≡ H1))(rs) ↔ (∀ r. r ∈ rs → (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 23:
modify(rs)(H0, H), r ∈ rs, ∀ r. r ∈ rs → (r ∈ H ↔ r ∈ H1) ∧ (r ∈ H → H[r] = H1[r]) ⊦ # rs = 0, rs = ∅, (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])

Rule argument

spec: <toplevel> name: agree seq: ⊦ ((H0 ≡ H1))(rs) ↔ (∀ r. r ∈ rs → (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [rs, H1, H0] → [rs, H1, H] flags: <all paths>

Additional information

Used terms: rs, H1, H