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Theorem div-two-intro
⊦ j % 2 = 0 ∧ j ≠ 0 → i / j = (i / 2) / j / 2
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: 14
Proof steps: 25
Used lemmas:
div-eq-zero
,
neg
,
div-twoodd
,
num-neg-01
,
mult-02
,
mod-mult-03
,
div-add1-pospos
,
nummult-ls-02
,
div-zero-02
,
zero
,
num-neg
,
div-twoodd-04
,
div-twoodd-03
,
nummult-ls
,
div-elim-negpos
,
div-elim-pospos
,
div-two-01
,
one
,
div-mult-num-01
,
modex
,
Used spec theorems:
int-mult
/
minus-left
Used simplifier rules:
int-abs
/
lels-01
int-abs
/
lsone
int-abs
/
sub-ls
int-abs
/
minus-add
int-abs
/
forward-le-04
int-basic1
/
minus-one
int-abs
/
numls-02
int-abs
/
neg-13
int-abs
/
abs-08
int-abs
/
elim-sub
int-abs
/
sub-eq
int-mult
/
eq-pos
int-abs
/
Sub-def
int-abs
/
neg-10
int-mult
/
abs-eqall
int-abs
/
abs-06
int-mult
/
zero-ge-add-01
int-abs
/
forward-le-01
int-abs
/
forward-le-05
int-basic1
/
lf-02
int-basic1
/
two-ls
int-basic2
/
eq
int-abs
/
lels
int-abs
/
lels-02
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-basic1
/
ls-01
int-basic1
/
lst-01
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
zero-gr
int-mult
/
zero-ge
int-abs
/
neg-02
int-mult
/
minus-left
int-mult
/
associativity
int-mult
/
zero-neq-01
int-mult
/
zero-ls
int-abs
/
zero-gels-01
int-abs
/
zero-gels-04
int-abs
/
neg
int-mult
/
commutativity