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Proof step 2 from proof At-in-out (previous step)

b ∈ st ⊦ st[a, d][b] = st[b], a ∈ st

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 3:
b ∈ st ⊦ b = a, st[a, d][b] = st[b], a ∈ st

Rule argument

fma: b = a

Additional information

Used simplifier rules: At-same: ⊦ st[a, d][a] = d;%notmemlookup: ⊦ ¬ a ∈ st → st[a] = (∅)[a]; Used formulas: b = a