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Theorem div-minus-onediff
⊦ i % j ≠ 0 ∧ j0 = j - 1 ∧ i < 0 ∧ 0 < j → (i - j0) / j = i / j - 1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div-minus255-256
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 10
Used lemmas:
div-zero-02
,
div-mult-03
,
mod-mult-04
,
div-add1-negneg
,
div-elim-negpos
,
Used spec theorems:
Used simplifier rules:
int-abs
/
sub-sub-04
int-basic1
/
forward-pos
int-mult
/
ls-same
int-basic2
/
lst-03
int-mult
/
ls-add
int-basic2
/
add-less
int-basic2
/
ls-01
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
/
forward-le-05
int-abs
/
lels-02
int-abs
/
lels
int-abs
/
mone-08
int-abs
/
zero-gels-01
int-basic1
/
lf-02
int-abs
/
numls-03
int-abs
/
zero-gels-04
int-abs
/
lsone
int-abs
/
sub-ls
int-mult
/
zero-ls
int-basic2
/
eq
int-abs
/
Sub-def
int-mult
/
zero-left
int-abs
/
abs-05
int-abs
/
abs-08
int-abs
/
subsub
int-abs
/
abs-16
int-abs
/
neg-13
int-basic2
/
zero-02
int-basic2
/
add-in
int-abs
/
sub-eq
int-abs
/
numadd
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
eq-dist
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
elim-sub