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Proof step 15 from proof min-delmin (previous step)

(s -- s.min).min = s.min, s.min ∈ s, s.max ∈ s ⊦ # s = 0, # s = 1, s = ∅, s = ∅ ++ s.min, s.max < s.min

User applied rule insert lemma

And obtained the following new goals

Proof step 16:
⊦ s ≠ ∅ → s.min ∈ s

Rule argument

spec: <toplevel> name: Min-in seq: ⊦ s ≠ ∅ → s.min ∈ s subst: [s] → [s -- s.min]

Additional information

Used simplifier rules: ⊦ s -- a = ∅ ↔ s = ∅ ∨ s = ∅ ++ a; (ws)% ⊦ a ∈ s -- b ↔ a ≠ b ∧ a ∈ s; (ws) Used terms: s -- s.min