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Proof step 9 from proof exnotempty (previous step)

⊦ ∃ a, d, st0. st = st0[a, d] ∧ ¬ a ∈ st0, ¬ a ∈ st ∧ st[a] = (∅)[a]

User applied rule cut formula

And obtained the following new goals

Proof step 10:
a ∈ st ⊦ ∃ a, d, st0. st = st0[a, d] ∧ ¬ a ∈ st0, ¬ a ∈ st ∧ st[a] = (∅)[a]

Rule argument

fma: a ∈ st

Additional information

Used simplifier rules: notmemlookup: ⊦ ¬ a ∈ st → st[a] = (∅)[a]; Used formulas: a ∈ st