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Theorem mult-def-any
⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
mult-a
,
mult-dist
,
mult-eq-same
,
mult-ls
,
mult-pos-02
,
square-abs
,
square-int-nlz
,
square-isSquare
,
square-ls
,
square-pos
,
square-pos-01
,
square-scale
,
square-sqrt
,
square-sqrt-02
,
Used by units in proved state:
decimal-complex-ops
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 36
Used lemmas:
mult-def
,
Used spec theorems:
decimal
/
intvalue-base
decimal
/
scale-base
int-div
/
modex
decimal
/
mkDecimal-rec
decimal
/
mkDecimal-zero
Used simplifier rules:
int-abs
/
abs-add-zero
int-abs
/
abs-abs-01
int-mult
/
one
int-div
/
div-mult-num
int-div
/
mod-zero-num
int-abs
/
abs-abs
int-abs
/
sub-add-01
nat-basic2
/
c
nat-basic2
/
a
int-mult
/
le-same-04
int-abs
/
lels
int-mult
/
abs-eqall
intnat
/
labs
nat-basic2
/
l
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero
decimal
/
scale-zero
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
Mult-zero
decimal
/
intvalue-zero