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Theorem div2-add-neg
⊦ j % 2 = 0 ∧ i ≤ 0 ∧ abs(i) ≤ j → (i + j) / 2 = (i - 1) / 2 + j / 2
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 12
Used lemmas:
div-mult-num
,
div-two
,
nummult-le-03
,
div-elim2
,
div-elim-pos
,
Used spec theorems:
int-abs
/
mone-07
int-abs
/
numadd-01
Used simplifier rules:
int-abs
/
elim-sub
int-abs
/
numle-02
int-abs
/
negle-13
int-abs
/
subsub
int-abs
/
abs-05
int-abs
/
mone-05
int-abs
/
numle-03
int-abs
/
lels-01
int-abs
/
zero-ge-01
int-abs
/
numadd-01
int-abs
/
Sub-def
int-abs
/
sub-ls
int-abs
/
mone-06
int-abs
/
lels-03
int-abs
/
forward-le-01
int-mult
/
zero-ge
int-abs
/
zero-gels-01
int-abs
/
zero-gels-04
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-mult
/
dist-rmerge
int-abs
/
lels-02
int-abs
/
abs-08
int-abs
/
neg-13
int-abs
/
numls-02
int-basic1
/
minus-one
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
add-zero
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-in
int-mult
/
zero-ls