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Theorem mod-zero-num

i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: div-div-pred-01, mod-by6, mod-next-square, mod-two-02,
Used by units in proved state: int-gcd,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas: mod-mult-04, modex,
Used spec theorems:
- Used simplifier rules:
  - int-mult/associativity
  - int-mult/commutativity