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Theorem align-down-add-ls
m ≠ 0 ⊦ align↓(n0 + n1, m) < n0 ↔ n0 % m + n1 < m ∧ n0 % m ≠ 0
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: 9
Proof steps: 19
Used lemmas:
aligndown-def
,
Used spec theorems:
nat-mult
/
dist
Used simplifier rules:
nat-basic
/
l-02
nat-mult
/
ls-02
nat
/
lez
nat-mult
/
zero-01
nat-basic
/
l-01
nat-basic
/
lf-01
nat
/
fle
nat-basic
/
l
nat-basic
/
lf
nat-basic
/
trans
nat-basic
/
succ
nat-mult
/
ls-08
nat
/
lels
nat
/
lep
nat-basic
/
zero
nat-mult
/
modeq-01
nat-basic
/
z-01
nat-basic
/
f
nat-div
/
mod-mult
nat-div
/
mod-eq
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-basic
/
a
nat-basic
/
c
nat-div
/
mult
nat-div
/
zero-01
nat-basic
/
add-base
nat
/
le-add
nat-mult
/
zero
nat
/
lez-01
nat-basic
/
zero-01
nat-div
/
div-elim