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Theorem mod-pred-neg
⊦ i % j - 1 ≠ ~ j ∧ i < 0 ∧ 0 < j → i % j = (i - 1) % j + 1
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: 4
Proof steps: 12
Used lemmas:
div-elim-negpos
,
Used spec theorems:
int-mult
/
modeqp-copied
Used simplifier rules:
int-abs
/
elim-sub
int-abs
/
numls-03
int-abs
/
neg-12
int-basic2
/
add-less
int-abs
/
forward-le-05
int-abs
/
lenls
int-basic2
/
ls
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
lels
int-abs
/
zero-gels-04
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
mone-05
int-abs
/
numle-03
int-abs
/
negle-07
int-abs
/
neg-15
int-abs
/
lels-02
int-abs
/
abs-08
int-abs
/
neg-13
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
zero-gels-01
int-basic1
/
numlsf
int-abs
/
forward-le-02
int-abs
/
zero-gels-03
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-ls
int-abs
/
sub-eq
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
add-in
int-abs
/
sub-add-01
int-abs
/
sub-le-01
int-abs
/
numleledel
int-abs
/
sub-ls
int-basic1
/
lst-01
int-abs
/
lsone
int-abs
/
lels-03