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Theorem congmod-inverse-smallest

gcd(i, j) = 1, 0 ≤ i, 0 < j ⊦ ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 12
Proof steps: 23
Used lemmas: mod-zero, mod-mult-add, mod-mod, mod-mult-law, mod-zero-01, mod-one, mod-pos-def, congmod-def, congmod-def-mod, mod-le-same, mod-pos, cong-one, cong-zero, congmod-inverse-pos,
Used spec theorems:
- int-div/mod-zero-05
- int-gcd/divides
Used simplifier rules: