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Theorem mod-neq
⊦ abs(j1) < abs(i) ∧ j1 ≠ 0 → i * j ≠ i * j0 + j1
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
int-gcd
,
int-div
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 10
Used lemmas:
eq-pos
,
modeqp-01
,
modeqp
,
associativity
,
eq-neg
,
modeqp-02
,
commutativity
,
modeqp-03
,
Used spec theorems:
int-abs
/
Abs-pos
Used simplifier rules:
int-abs
/
numls-03
int-basic2
/
ls
int-abs
/
lenls
int-abs
/
sub-ls
int-abs
/
neg-15
int-abs
/
forward-lels
int-abs
/
neg
int-abs
/
neg-07
int-abs
/
lels-01
int-basic1
/
forward-pos
int-basic2
/
add-less
int-basic2
/
ls-01
int-basic2
/
succ-01
int-abs
/
forward-le-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-le-05
int-basic1
/
ls-01
int-abs
/
zero-gels-01
int-basic1
/
lst-01
int-basic1
/
irref
int-abs
/
abs-16
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
absls
int-basic1
/
lf-02
int-abs
/
anti
int-abs
/
lels
int-abs
/
lels-02
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
zero-gels-03
int-abs
/
abs-08
int-abs
/
neg-13