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Theorem modeqp-03
i * j + j0 = i0 * j + j1, j < 0, j0 ≤ 0, j < j0, j1 ≤ 0, j < j1 ⊦ i = i0 ∧ j0 = j1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
mod-neq
,
Used by units in proved state:
int-div
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 5
Used lemmas:
eq-neg
,
commutativity
,
associativity
,
minus-left
,
modeqp-01
,
Used spec theorems:
int-abs
/
Abs-neg
Used simplifier rules:
int-abs
/
forward-le-04
int-abs
/
neg-07
int-abs
/
sub-add-01
int-abs
/
sub-eq
int-abs
/
lels-02
int-abs
/
abs-08
int-basic2
/
add-in
int-abs
/
numls-03
int-basic2
/
succ-01
int-abs
/
zero-gels-04
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-basic1
/
lf-01
int-abs
/
sub-ls
int-abs
/
zero-gels-03
int-abs
/
neg-06
int-abs
/
neg-15
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-le-01
int-basic2
/
add-zero-rev
int-abs
/
lels-03
int-abs
/
Abs-pos
int-abs
/
lels
int-abs
/
anti
int-abs
/
forward-le-01
int-abs
/
forward-lele
int-basic1
/
lf-02
int-abs
/
forward-lsle