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Theorem mod-mult-pos-01

⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (j * i + i0) % j = i0 % j

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: even-or-succ-even, mod-mult-pos-02, modmod-add2-negpos-neg, modmod-add2-negpos-pos,
Used by units in proved state: int-gcd,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: mod-mult-pos, div-elim-pospos,
Used spec theorems:
- Used simplifier rules: