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Theorem is-min

⊦ s ≠ ∅ → (s.min = a ↔ a ∈ s ∧ (∀ b. b ∈ s → ¬ b < a))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: min-less, minmax-04, Max-max, Min-min, Min-in, Max-in,
Used spec theorems:
- Used simplifier rules:
  - weakord/tord/irreflexivity
  - set-basic/ne-01
  - set-basic/size-zero-01
  - tord/sls