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Theorem mod-abs-neg-div
⊦ i < 0 ∧ j < 0 ∧ i % j = 0 → i |%| abs(j) = i |%| 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: 2
Proof steps: 4
Used lemmas:
mod-pos-def
,
mod-mult
,
Used spec theorems:
int-div
/
modex
Used simplifier rules:
int-abs
/
forward-le-02
int-abs
/
abs-08
oelem
/intlista/
transitivity
int-abs
/
forward-le-05
int-mult
/
zero-ls-01
int-div
/
mod-neg
int-div
/
mod-mult-04
int-mult
/
associativity
int-mult
/
commutativity