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Proof step 7 from proof rem-write-other (previous step)

¬ a0 ∈ s, a ∈ s ⊦ s = ∅, # s = 0, (a0 ∈ st[a, d] \ s ↔ a0 ∈ st \ s) ∧ st[a, d][a0] = (st \ s)[a0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
a ∈ s ⊦ s = ∅, # s = 0, a0 ∈ s, (a0 ∈ st → a0 ∈ st[a, d]) ∧ st[a, d][a0] = st[a0]

Rule argument

Additional information

Used simplifier rules: Diff-ext: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s;%Diff-get: ⊦ ¬ a ∈ s → (st \ s)[a] = st[a];%In-insert: ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st; from specification store