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Proof step 27 from proof congmod-inverse-pos (previous step)

(i * i1) |%| j = 1, gcd(i, j) = 1, i0 < 0, ≡mod(i * i0, 1, j), 0 ≤ j, 0 ≤ i, 0 < i1, 0 < j, 0 ≤ i1 ⊦ ≡mod(i * i1, 1, j), ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mod inst: name: congmod-def-mod seq: ⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j) subst: [j, i0, i] → [j, 1, i * i1] flags: rewrite, current

Additional information

Used terms: j, 1, i * i1