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Proof step 5 from proof rem-write (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 6:
⊦ a0 = a, a ∈ s, (a0 ∈ st[a, d] \ s ↔ a0 ∈ (st \ s)[a, d]) ∧ (st[a, d] \ s)[a0] = (st \ s)[a, d][a0]

Rule argument

fma: a0 = a

Additional information

Used simplifier rules: Diff-ext: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s;%Diff-get: ⊦ ¬ a ∈ s → (st \ s)[a] = st[a];%insin: ⊦ a ∈ st[a, d]; from specification store%At-same: ⊦ st[a, d][a] = d; from specification store Used formulas: a0 = a