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Theorem le-div-to-mult

m0 ≠ 0 ⊦ n ≤ m / m0 ↔ n * m0 ≤ m

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: div-le, div-le-01, le, nummult-le-01, square-interval, two-le-01, two-le-04, two-loup-01, two-loup-04, two-ls-03, two-padd,
Used by units in proved state: nat-pair,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 12
Used lemmas: div-elim,
Used spec theorems:
- nat-basic2/addex
- nat-mult/dist
Used simplifier rules: