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Proof step 6 from proof rem-write (previous step)

⊦ a0 = a, a ∈ s, (a0 ∈ st[a, d] \ s ↔ a0 ∈ (st \ s)[a, d]) ∧ (st[a, d] \ s)[a0] = (st \ s)[a, d][a0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ a0 = a, a ∈ s, (a0 ∈ st[a, d] \ s ↔ a0 ∈ st \ s) ∧ (st[a, d] \ s)[a0] = (st \ s)[a0]

Rule argument

Additional information

Used simplifier rules: At-other: ⊦ a ≠ b → st[b, d][a] = st[a]; from specification store%in-neq: ⊦ a ≠ b → (a ∈ st[b, d] ↔ a ∈ st); from specification store