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Theorem modmod-pos
⊦ 0 ≤ i ∧ 0 < j ∧ 0 < j0 → i % (j * j0) = i % j + (i / j) % j0 * j
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: 7
Proof steps: 16
Used lemmas:
mod-same
,
mod-zero-03
,
mod-mult-04
,
mod-mult-02
,
mod-add-pos
,
div-elim-pospos
,
Used spec theorems:
int-mult
/
mod-neq
int-mult
/
modlsp
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-basic2
/
add-in
int-mult
/
eq-dist
int-mult
/
zero-ge
int-abs
/
zero-gels-04
int-mult
/
modzero-03
int-abs
/
lels
int-mult
/
zero-ge-add
int-mult
/
zero-gr
int-abs
/
ler
int-mult
/
le-pos
int-mult
/
zero-eq
int-mult
/
Mult-zero
int-abs
/
absle
int-abs
/
abs-16
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
eq-nonzero
int-mult
/
associativity
int-basic1
/
irref
int-abs
/
lels-02
int-abs
/
lels-03
int-mult
/
commutativity