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Theorem div-minus-onediff-01
⊦ i % j = 0 ∧ j0 = j - 1 ∧ i < 0 ∧ 0 < j → (i - j0) / j = i / j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div-minus255-256-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 17
Used lemmas:
one-02
,
mod-div-zero
,
one-01
,
div-eq-zero
,
div-add1-negpos-neg-01
,
div-add-rew
,
mod-mult-04
,
div-add-both
,
div-mult-03
,
modex
,
one
,
mod-one
,
mod-ls-same-02
,
Used spec theorems:
Used simplifier rules:
int-abs
/
negle-07
int-abs
/
abs-08
int-abs
/
numsub
int-abs
/
forward-le-05
int-abs
/
sub-sub-04
int-basic2
/
ls
int-basic2
/
succ-01
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
forward-le-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
zero-gels-03
int-mult
/
ls-same
int-abs
/
zero-gels
int-abs
/
lels-01
int-mult
/
zero-ge
int-abs
/
numadd
int-basic2
/
add-zero-rev
int-basic2
/
eq
int-abs
/
lels
int-abs
/
bet
int-abs
/
numls-03
int-mult
/
zero-ls
int-abs
/
forward-lsle
int-mult
/
ls-same-03
int-abs
/
lsone
int-abs
/
lels-03
int-abs
/
zero-gels-01
int-basic1
/
lf-02
int-basic2
/
add-in
int-abs
/
sub-eq
int-abs
/
sub-add-01
int-mult
/
eq-one
int-abs
/
abs-16
int-mult
/
eq-succ
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
elim-sub