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Theorem ls-pos

⊦ 0 < i → (i * j < i * j0 ↔ j < j0)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by: auxexdivmod, eq-nonzero, est-nle, exdivmodpos, le-pos, ls-neg, ls-pos-01, ls-same, ls-sub, modlep-04, modlsp, modneqp, mult-add-greater, mult-gt-both, mult-sub-less, noeth-ls-pos, noeth-modlep, numls-10, ple-pos, pls-pos, pls-pos-01, pls-pos-02, pnls-negpos, pnls-posneg, short-mult-max, zero-ls,
Used by units in proved state: int-pot, int-gcd, int-div, intnat,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 11
Used lemmas: dist-lsplit, one, dist-rsplit, zero-gr, commutativity, associativity, Mult-zero,
Used spec theorems:
- Used simplifier rules: