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Theorem mod-abs-neg-neg
⊦ i < 0 ∧ j < 0 ∧ i % j ≠ 0 → i |%| abs(j) = i |%| j - 2 * 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-neg-def
,
Used spec theorems:
Used simplifier rules:
int-abs
/
sub-eq
int-abs
/
abs-08
int-basic1
/
lst-01
int-div
/
mod-grz-02
int-abs
/
forward-le-02
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numeq-02
int-abs
/
zero-gels-01
int-div
/
mod-neg
int-abs
/
neg-03
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels
int-div
/
mod-ngez-01