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Proof step 7 from proof dom-max-in (previous step)

(dom st0 = ∅ ⊃ m;(m < (dom st0).max ⊃ (dom st0).max;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 8:
(st0 = ∅ ⊃ m;(m < (dom st0).max ⊃ (dom st0).max;m)) < n, n ∈ st0[m, d], (∃ n. (dom st0).max < n ∧ n ∈ st0) → st0 = ∅ ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ dom st = ∅ ↔ st = ∅; (s)