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Theorem gcd-div-rest

⊦ abs(j0) < gcd(i, j) → (i = i1 * gcd(i, j) + j0 ↔ i = i1 * gcd(i, j) ∧ j0 = 0)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: gcd-div-gcd-pos,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 8
Used lemmas: gcd-abs, divides, gcd-div1,
Used spec theorems:
- int-mult/mod-neq
Used simplifier rules: