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Theorem mod2-add-neg
⊦ j % 2 = 0 ∧ i ≤ 0 ∧ abs(i) ≤ j → (i + j) % 2 = ~ i % 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: 10
Used lemmas:
mod-two-03
,
div-elim2
,
mod-two-02
,
div-elim-pos
,
mod-neg-01
,
Used spec theorems:
Used simplifier rules:
int-abs
/
negeq
int-abs
/
lels
int-abs
/
abs-zero
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
forward-le-05
int-mult
/
zero-ge
int-abs
/
negle-13
int-basic2
/
add-less
int-mult
/
ls-pos
int-basic2
/
ls-01
int-abs
/
zero-gels-04
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
forward-le-01
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
/
zero-gels-01
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-abs
/
minus-add
int-abs
/
sub-eq
int-mult
/
neq-two
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
mone-06
int-abs
/
sub-le-01
int-abs
/
leone
int-mult
/
zero-gr
int-basic2
/
add-zero