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Theorem modmod-add-law-pos
0 < j ⊦ (i % j + i0 % j) % j = (i + i0) % j ∨ (i % j + i0 % j) % j = (i + i0) % j + j ∨ (i % j + i0 % j) % j = (i + i0) % j - j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
modmod-add-law
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 19
Used lemmas:
mod-less-01
,
mod-lsz
,
modmod-add-case
,
Used spec theorems:
int-basic2
/
add-c
int-mult
/
numls-13
Used simplifier rules:
int-basic2
/
add-in
int-abs
/
forward-le-05
int-mult
/
numsub
int-abs
/
sub-add-01
int-mult
/
numsucc
int-mult
/
zero-neq-01
int-basic2
/
eq
int-mult
/
add-mult-two
int-abs
/
sub-sub
int-abs
/
sub-eq
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numeq-02