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Proof step 9 from proof dom-max-in (previous step)

st0 = ∅, m < n, n ∈ st0[m, d], (∃ n. (dom st0).max < n ∧ n ∈ st0) → st0 = ∅ ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
m < n, n ∈ (∅)[m, d] ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n ∈ ∅; (s)% ⊦ dom ∅ = ∅; (s)