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Proof step 34 from proof geom-mod (previous step)

(i - 1) * ~1 ≠ 0, (i - 1) * ~1 ≠ 0, 1 - i ^ i0 = ~((i - 1) * j0), 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, ((i - 1) * ~1 - ((i - 1) * j0) * i) % (i - 1) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-sub-merge seq: ⊦ i * j - i * j0 = i * (j - j0) subst: [j0, j, i] → [i * j0, ~1, i - 1] flags: rewrite

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i * j0, ~1, i - 1