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Theorem square-neq-any-pos-02

0 < i, 0 < j, 0 < j0, gcd(j, j0) = 1, j * j = i * j0 * j0 ⊦ ∃ i0. i = i0 * i0

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: square-neq-any-pos-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 39
Proof steps: 58
Used lemmas: gcd-same-01, square-prime-eq, div-mult, gcd-mult, prime-divides, prime-small, gcd-mult-01, gcd-abs, not-less-gcd, gcd-zero-zero, gcd-less-eq-zero, div-gcd-not-neg, gcd-div-gcd, gcd-com, gcd-zero-04, gcd-div-shift, prime-not-neg-01, prime-not-neg, prime-one, prime-abs, divides, prime-def-prime, square-neq-pos-h,
Used spec theorems:
Used simplifier rules: