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Theorem mod-add-pos

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

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: mod-add1-pospos, mod-mult-pos, mod-shift, modmod-add-04, modmod-pos,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 7
Used lemmas: modeq-pos, div-elim-pos, mod-less-01,
Used spec theorems:
- int-mult/commutativity
Used simplifier rules: