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Theorem square-le

⊦ i * i ≤ j * j ↔ abs(i) ≤ abs(j)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: square-ex, square-le-04, square-ls-02, square-one-le,
Used by units in proved state: int-gcd, int-square,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 4
Used lemmas: commutativity, associativity, square-ls,
Used spec theorems:
- int-abs/forward-lsle
Used simplifier rules: