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Proof step 30 from proof congmod-inverse-smallest (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i1, j] flags: rewrite

Additional information

Used simplifier rules: mod-mult-add: ⊦ 0 < j → (i + i0 * j) |%| j = i |%| j;%mod-zero: ⊦ 0 ≤ i ∧ i < j → i |%| j = i;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i1, j