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Theorem mod-rew
j ≠ 0 ⊦ i % j = i - i / j * j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div2one-01
,
divmult
,
mod-ls-same
,
mod-mult
,
mod-mult-02
,
mod-mult-04
,
mod-neg
,
mod-neg-01
,
mod-same
,
mod-twoodd
,
mod-zero-01
,
mod-zero-04
,
mod-zero-06
,
modeq-pos
,
one-01
,
Used by units in proved state:
int-pot
,
int-gcd
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 0
Proof steps: 1
Used lemmas:
divmod-rew
,
Used spec theorems:
Used simplifier rules:
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-abs
/
sub-eq