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Theorem add-scale-neq
⊦ dec_i.scale ≠ dec_j.scale → (dec_i + dec_j).scale = max(dec_i.scale, dec_j.scale)
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: 37
Proof steps: 70
Used lemmas:
add-def
,
Used spec theorems:
decimal
/
mkDecimal-maxScale-nle-scale
decimal
/
mkDecimal-maxScale-le-scale
decimal
/
maxScale-pot10-add
int-basic2
/
add-c
int-abs
/
add-shift
int-pot
/
Pot-pos
decimal
/
intvalue-mod-10
int-pot
/
pot-add-min
decimal
/
maxScale-pot10-02
decimal
/
maxScale-base
int-pot
/
pot-mod-add-zero
int-min
/
Min-right
Used simplifier rules:
int-abs
/
sub-eq
int-abs
/
neg-10
int-div
/
mod-neg-01
int-abs
/
neg-15
int-abs
/
neg-06
int-abs
/
sub-pred
int-abs
/
sub-sub
int-div
/
mod-zero-num
int-abs
/
lels
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
lels-03
int-abs
/
forward-lels
int-abs
/
le-add
int-pot
/
pot-mod-add-zero
int-basic2
/
eq
int-abs
/
forward-le-04
int-abs
/
absle
int-abs
/
abs-12
int-basic2
/
add-in
int-abs
/
lels-01
int-abs
/
forward-le-01
int-mult
/
Mult-zero
decimal
/
maxScale-zero
int-abs
/
zero-gs
int-abs
/
zero-gels-01
int-min
/
Max-left
decimal
/
intvalue-mod-10
int-abs
/
sub-ls-01
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-basic1
/
ls-01
int-basic2
/
ls-01
int-basic2
/
add-zero
int-basic1
/
lst-01
int-min
/
Max-right
int-min
/
max-a
int-min
/
max-c
int-abs
/
sub-sub-03
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
lels-02
int-basic2
/
ls
decimal
/
scale-not-neg
int-basic2
/
add-a
int-basic2
/
add-c
int-min
/
Min-left
int-min
/
min-a
int-min
/
min-c
int-abs
/
zero-gels-04