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Theorem congmod-def-mod-02

⊦ i < 0 ∧ i0 < 0 ∧ j ≠ 0 → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 26
Proof steps: 42
Used lemmas: mod-pos-def, mod-neg-def, congmod-def-mod, congmod-mod-abs,
Used spec theorems:
- int-abs/Abs-pos
- int-div/mod-abs
Used simplifier rules: