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Proof step 20 from proof modify-agree (previous step)

modify(rs)(H0, H), ((H ≡ H1))(rs) ⊦ ∀ r. r ∈ rs → (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
modify(rs)(H0, H), r ∈ rs, ((H ≡ H1))(rs) ⊦ # rs = 0, rs = ∅, (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ rs ≠ ∅ → # rs ≠ 0; (forward) from specification set-basic[refset]%ne-01: ⊦ r ∈ rs → rs ≠ ∅; (forward) from specification set-basic[refset]