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Theorem sub-def-any
⊦ mkDecimal(i, j) - mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
less-def-any
,
ls-zero
,
sub-add
,
sub-same
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 31
Proof steps: 57
Used lemmas:
sub-zero
,
sub-def
,
Used spec theorems:
decimal
/
mkDecimal-rec
decimal
/
intvalue-base
decimal
/
scale-base
decimal
/
mkDecimal-zero
decimal
/
getint-neg
decimal
/
mkDecimal-negated
int-div
/
modex
decimal
/
mkDecimal-enlarge
int-abs
/
Abs-pos
int-abs
/
lels-02
int-mult
/
dist-sub-split
int-pot
/
Pot-pos
Used simplifier rules:
int-abs
/
sub-zero-01
int-abs
/
abs-abs
int-div
/
div-mult-num
int-abs
/
abs-zero
int-abs
/
abs-add-pos
int-abs
/
abs-add-zero
int-abs
/
forward-le-05
int-abs
/
lels-01
int-abs
/
Sub-def
int-mult
/
eq-pos
nat-basic2
/
c
nat-basic2
/
a
int-div
/
abs-div10-le
int-abs
/
lels
int-div
/
abs
intnat
/
labs
nat-basic2
/
l
int-abs
/
neg-06
decimal
/
scale-zero
int-mult
/
Mult-zero
decimal
/
intvalue-zero
int-mult
/
minus-left
decimal
/
eq-same
int-abs
/
abs-03
int-abs
/
forward-le-04
int-abs
/
lsone
int-abs
/
sub-ls
int-abs
/
neg-15
int-abs
/
minus-02
int-abs
/
abs-08
int-basic2
/
add-zero
int-mult
/
one
int-abs
/
abs-06
int-abs
/
sub-pred
int-mult
/
eq-nonzero
int-mult
/
neq-not-zero
int-basic2
/
add-in
int-abs
/
sub-eq
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
sub-add-01
int-mult
/
commutativity
int-mult
/
associativity