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Theorem le-neg

⊦ r < 0.r → (r * r0 ≤ r * r1 ↔ r1 ≤ r0)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: invmult-le-neg, le-abs, le-neg-01, le-negint, le-same-03, pnle-neg, square-le,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 11
Used lemmas: mult-com, mult-ass, ls-neg, minus-left, distr, order,
Used spec theorems:
- real-abs/gr-def
- real-basic/neg-09
Used simplifier rules: