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Theorem add-scale-eq
⊦ dec_i.scale = dec_j.scale ∧ dec_i.int + dec_j.int ≠ 0 → (dec_i + dec_j).scale ≤ dec_i.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: 6
Proof steps: 11
Used lemmas:
add-def
,
Used spec theorems:
decimal
/
mkDecimal-maxScale-nle-scale
decimal
/
mkDecimal-maxScale-le-scale
int-abs
/
Abs-pos
int-mult
/
dist-lsplit
decimal
/
maxScale-pot10-nls
Used simplifier rules:
int-mult
/
add-mult-two
int-abs
/
lenls
int-abs
/
sub-ls-01
int-mult
/
abs-eqall
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numls-08
int-abs
/
lels-01
decimal
/
scale-not-neg