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Proof step 30 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 ⊦ 1 = 1 |%| j, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ 0 ≤ i ∧ i < j → i |%| j = i

Rule argument

spec: int-mod inst: name: mod-zero seq: ⊦ 0 ≤ i ∧ i < j → i |%| j = i subst: [j, i] → [j, 1] flags: rewrite, current

Additional information

Used simplifier rules: mod-one: ⊦ i |%| 1 = 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd Used terms: j, 1