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

i * i0 = i1 + 1, gcd(i, j) = 1, 0 ≤ i0, 0 < i, i0 |%| j < j, i0 |%| j < i0, 0 ≤ i0 |%| j, 0 < j, j ≤ i0, 0 < i0, j | i1 ⊦ i = 0, j = 0, (i * i0 |%| j) |%| j = 1 % j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mod-zero-05 seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [j, 1] flags: rewrite

Additional information

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