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Theorem pot-add-min
⊦ 0 ≤ j ∧ 0 ≤ j0 → i * 10 ^ j + i0 * 10 ^ j0 = (i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0)
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: 5
Proof steps: 8
Used lemmas:
eq-pos
,
Pot-neg
,
pot-dist-pos
,
Used spec theorems:
int-mult
/
dist-lsplit
int-mult
/
associativity
int-min
/
Min-right
Used simplifier rules:
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
zero-gels-03
int-abs
/
abs-08
int-abs
/
sub-sub-03
int-mult
/
one
int-abs
/
lenls
int-min
/
Min-left
int-mult
/
eq-nonzero
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
neq-not-zero
int-abs
/
forward-le-01
int-basic2
/
add-in
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-le-01
int-basic2
/
add-zero-rev
int-abs
/
zero-gels-04
int-abs
/
lels-01
int-min
/
min-03
int-min
/
min-a
int-min
/
min-c