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Theorem congmod-inverse-pos

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

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 24
Used lemmas: mod-one, mod-zero, congmod-def-mod, rem-mod-pos, cong-zero, cong-one, cong-same, congmod-inverse,
Used spec theorems:
- int-gcd/gcd-mod-one-01
- int-abs/le-rec
Used simplifier rules: