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Theorem ins-less-first

⊦ ordered≤(x) ∧ x ≠ [] ∧ x.head < a → ins≤(a, x) = x.head + ins≤(a, x.tail)

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: 0
Proof steps: 5
Used lemmas: ins-n, app-01, cons-02,
Used spec theorems:
- Used simplifier rules:
  - list/c
  - list-data/elim-add
  - list/a
  - list/e-01
  - list/c-06