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Theorem isSquare-mult-aux
j0 * j0 = j * i * i, 0 < j0, 0 < j, 0 < i ⊦ i = 0, isSquare(j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
isSquare-mult
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 51
Proof steps: 73
Used lemmas:
prime-not-neg
,
max_prime_divisor-prime
,
prime-small
,
max_prime_divisor-divides
,
divides
,
prime-divides
,
prime-mult-eq
,
Used spec theorems:
int-mult
/
associativity
int-mult
/
eq-nonzero
int-abs
/
Abs-pos
int-mult
/
numle-07
int-mult
/
mult-pos
int-square
/
isSquare-def
Used simplifier rules:
int-mult
/
eq-same-02
int-mult
/
eq-pos
int-abs
/
lels-01
int-basic1
/
two-ls
int-mult
/
eq-one
int-mult
/
square-abs
int-square
/
isSquare-one
int-mult
/
zero-eq
int-mult
/
neq-not-zero
int-abs
/
abs-06
int-abs
/
forward-le
intnat
/
labs
int-basic1
/
ls-01
int-mult
/
zero-ge
int-abs
/
sub-le-01
int-basic2
/
add-zero-rev
int-abs
/
bet
int-mult
/
one-01
int-mult
/
eq-nonzero
int-abs
/
abs-08
int-abs
/
negle-07
int-basic1
/
lf-01
int-basic1
/
trans
int-abs
/
forward-le-02
int-basic2
/
ls
int-abs
/
zero-gels-01
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
succ-01
int-mult
/
ls-same-03
int-abs
/
lsone
int-mult
/
zero-gr-01
int-mult
/
zero-ls-01
int-abs
/
forward-le-04
int-mult
/
square-lez
int-mult
/
zero-gr-03
int-abs
/
lels-02
int-basic1
/
lst-01
int-mult
/
zero-gr
int-abs
/
lels
int-abs
/
anti
int-abs
/
forward-le-05
int-abs
/
forward-lels
int-mult
/
zero-neq-01
int-mult
/
zero-left
int-basic1
/
lf-02
int-mult
/
square-eq
int-mult
/
abs-eqall
int-abs
/
abs-16
int-mult
/
associativity
int-mult
/
commutativity
int-square
/
isSquare-square