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Proof step 6 from proof max-del (previous step)

s.max < (s -- a).max ⊦ s = ∅ ++ a, (s -- a).max ∈ s

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ s ≠ ∅ ∧ s ⊆ s0 → s.max ∈ s0

Rule argument

spec: <toplevel> name: max-subset-01 seq: ⊦ s ≠ ∅ ∧ s ⊆ s0 → s.max ∈ s0 subst: [s0, s] → [s, s -- a] flags: <all paths>

Additional information

Used simplifier rules: ⊦ s -- a = ∅ ↔ s = ∅ ∨ s = ∅ ++ a; (ws)% ⊦ s -- a ⊆ s; (s)% ⊦ ∅ ≠ s ++ a; (s)% ⊦ ∅ -- a = ∅; (s)% ⊦ ¬ a < a; (s) Used terms: s, s -- a