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Theorem div-add-nosucc
⊦ 1 < j ∧ 0 ≤ i ∧ i % j = 0 → (i + (j - 1)) / j = i / j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div-add-nosucc-neg
,
div-add1-negpos-neg-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 9
Used lemmas:
div-eq-zero
,
mod-mult-04
,
div-add-pos
,
div-mult-03
,
modex
,
Used spec theorems:
Used simplifier rules:
int-basic1
/
forward-pos
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
numsub
int-abs
/
sub-add-01
int-abs
/
zero-gels-04
int-mult
/
zero-ge
int-abs
/
leone
int-abs
/
sub-le-01
int-mult
/
commutativity
int-mult
/
associativity
int-basic2
/
eq
int-abs
/
forward-le-05
int-abs
/
numls-02
int-abs
/
numadd-01
int-basic2
/
add-zero-rev
int-abs
/
numadd
int-basic2
/
zero-02
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
succ-02
int-abs
/
lels-01
int-basic1
/
irref