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Theorem square-le

⊦ r * r ≤ r0 * r0 ↔ abs(r) ≤ abs(r0)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: square-ge-one, square-le-one, square-ls, square-ls-02,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 44
Proof steps: 72
Used lemmas: ls-pos-01, ls-forward, zero-ls-01, ls-pos, ls-neg, zero-le, le-pos-01, zero-le-01, mult-zero, le-pos, ple-pos, le-neg-01, minus-left, mult-com, mult-ass, le-neg, abs-ite,
Used spec theorems:
Used simplifier rules: