[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 21 from proof congmod-inverse (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 23:
(abs(i) * i0) % abs(j) = 1, gcd(i, j) = 1, 0 < i0 ⊦ j | abs(i * i0 - 1), ∃ i0. ≡mod(i * i0, 1, j)

Rule argument

spec: int-mod inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [j, 1, i * i0] flags: rewrite, current

Additional information

Used terms: j, 1, i * i0