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Theorem square-sqrt
⊦ mkDecimal(0, 0) ≤ dec → mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) = dec
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
square-sqrt-01
,
Used by units in proved state:
decimal-complex-ops
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 31
Used lemmas:
mult-def-any
,
le-zero
,
Used spec theorems:
decimal
/
intvalue-base
int-div
/
modex
decimal
/
intvalue-rec
decimal
/
scale-rec
int-abs
/
Abs-pos
int-mult
/
dist-sub-split
decimal
/
mkDecimal-rec
decimal
/
scale-base
int-square
/
inverse-ii
decimal
/
mkDecimal-scale-not-neg
Used simplifier rules:
int-abs
/
forward-le-01
int-mult
/
add-mult-two
int-mult
/
zero-gr
int-mult
/
neq-two
int-abs
/
sub-eq
int-mult
/
zero-neq-01
int-mult
/
zero-eq
int-abs
/
abs-08
int-abs
/
minus-02
int-abs
/
neg-15
int-abs
/
num-subadd
int-abs
/
neg-06
int-abs
/
abs-zero
int-abs
/
lsone
int-div
/
nummult-ls
int-abs
/
sub-ls
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
sub-sub
int-abs
/
lels-01
int-basic1
/
ls-01
intnat
/
labs
int-abs
/
lels
int-mult
/
le-same
int-abs
/
abs-abs
int-div
/
mod-zero-num
int-abs
/
forward-le-05
int-abs
/
lels-02
decimal
/
eq-zero
decimal
/
scale-zero
int-square
/
zero-01
int-mult
/
square-zero
int-abs
/
abs-07
int-mult
/
two-zero
int-gcd
/
mod-square-10
int-mult
/
one
int-div
/
div-mult-num
int-mult
/
commutativity
int-mult
/
associativity
int-abs
/
abs-01
int-mult
/
abs-eqall
decimal
/
eq-same
int-abs
/
abs-16