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Theorem i2n-mod
⊦ 0 ≤ i ∧ 0 < j → i→n(i % j) = i→n(i) % i→n(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: 4
Proof steps: 10
Used lemmas:
labs-01
,
abs-zero
,
i2n-mult
,
add-01
,
Used spec theorems:
nat-div
/
mod-eq
Used simplifier rules:
int-abs
/
forward-le-05
int-div
/
div-elim-pospos
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
zero-ge-add
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-ge
int-abs
/
zero-gels-04
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
forward-le-01
nat-basic2
/
c
nat-basic2
/
a
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-div
/
mod-mult
int-abs
/
lenls
nat
/
lels
int-abs
/
abs-16
int-abs
/
absle
int-abs
/
lels-03