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Theorem add
0 ≤ i, 0 ≤ j ⊦ i→n(i) + i→n(j) = i→n(i + j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
add-01
,
i2np
,
natpos
,
sub-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 11
Used lemmas:
rax-04
,
Int2nat-pos
,
Used spec theorems:
Used simplifier rules:
int-basic2
/
succ-01
int-abs
/
mone-08
int-abs
/
forward-lsle
int-abs
/
forward-le-02
nat-basic2
/
add-base
int-abs
/
forward-le-05
int-abs
/
leone
int-abs
/
sub-le-01
int-abs
/
sub-add-01
int-abs
/
sub-pred
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
numleledel-01
int-abs
/
numle-02
int-abs
/
zero-gels-04
int-abs
/
numsub
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
nat-basic2
/
eq-01
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
lels-01
int-abs
/
zero-gs