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Proof step 16 from proof geom-mod (previous step)

1 - i ≠ 0, 1 - i ^ i0 = j0 * (1 - i), 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i0 + 1) → 0 ≤ j0 → (1 - i ^ j0) % (1 - i) = 0 ∨ i = 1 ⊦ i = 1, ~1 = i0, ((j0 * (1 - i)) * i - (i - 1)) % (1 - i) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
j ≠ 0 ⊦ i % ~ j = i % j
Proof step 18:
1 - i ≠ 0, 1 - i ≠ 0, 1 - i ^ i0 = j0 * (1 - i), 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i0 + 1) → 0 ≤ j0 → (1 - i ^ j0) % (1 - i) = 0 ∨ i = 1 ⊦ i = 1, ~1 = i0, ((j0 * (1 - i)) * i - (i - 1)) % ~(1 - i) = 0

Rule argument

spec: int-div inst: name: mod-neg seq: j ≠ 0 ⊦ i % ~ j = i % j subst: [j, i] → [1 - i, (j0 * (1 - i)) * i - (i - 1)] flags: rewrite

Additional information

Used terms: 1 - i, (j0 * (1 - i)) * i - (i - 1)