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Proof step 3 from proof min-ins-04 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ a < s.min ∧ s ≠ ∅ → (s ++ a).min = a

Rule argument

spec: <toplevel> name: min-insert seq: ⊦ a < s.min ∧ s ≠ ∅ → (s ++ a).min = a subst: [a, s] → [a, s] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ b < a → (a < b ↔ a ≠ b); (ss)% ⊦ a ∈ s → s ++ a = s; (s) Used terms: a, s