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Proof step 17 from proof congmod-inverse-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: le-rec seq: ⊦ i ≠ j → (i ≤ j ↔ i ≤ j - 1) subst: [j, i] → [1, j] flags: rewrite

Additional information

Used simplifier rules: cong-zero: ⊦ ≡mod(i, j, 0) ↔ i = j;%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%gcd-zero-04: ⊦ gcd(i, 0) = abs(i); from specification int-gcd%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 1, j