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Theorem gcd-max
⊦ i0 | i ∧ i0 | j ∧ (i ≠ 0 ∨ j ≠ 0) → i0 ≤ gcd(i, j)
Type: An axiom
Validity: The proof is valid.
Features: nokodkodax,
Comment: if i = 0 ∧ j = 0, every i0 divides i and j, hence gcd must be greater than any number and the axiom would produce an inconsistent spec.
Used by:
gcd-abs-rew-02
,
gcd-com
,
gcd-div-gcd-pos
,
gcd-less
,
gcd-pos
,
gcd-same
,
gcd-zero-04
,
Used by units in proved state:
Proof exists?: No