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Theorem cong-equiv
⊦ m ≠ 0 → (m | dist(n, n0) ↔ n % m = n0 % m)
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: 16
Proof steps: 26
Used lemmas:
divi-mult
,
Divides
,
dist-snd
,
dist-fst
,
Used spec theorems:
nat-mult
/
dist-sub
Used simplifier rules:
nat
/
lels-01
nat-basic1
/
ls-02
nat-basic2
/
l-01
nat
/
lels-03
nat-mult
/
mult-base
nat-basic2
/
z
nat-mult
/
ls
nat-basic2
/
l-02
nat
/
eq-01
nat
/
elim-sub
nat
/
lep
nat-div
/
mod-ls
nat-basic1
/
lf-02
nat-div
/
mod-mult
nat-basic2
/
eq-01
nat-basic2
/
a
nat-basic2
/
c
nat-basic1
/
f
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-basic1
/
less-1
nat-div
/
div-elim