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Proof step 33 from proof geom-mod (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 34:
1 - i ^ i0 = ~((i - 1) * j0), ~(i - 1) = (i - 1) * ~1, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i0 + 1) → 0 ≤ j0 → (1 - i ^ j0) % (1 - i) = 0 ∨ i = 1 ⊦ (~(i - 1) - ((i - 1) * j0) * i) % (i - 1) = 0, ~1 = i0, i = 1, ~(i - 1) = 0

Rule argument

fma: ~(i - 1) = (i - 1) * ~1

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ i + ~ j = i - j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ~(i - 1) = ~ i + 1; (s)% ⊦ i * ~1 = ~ i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i + (j - i) = j; (s) Used formulas: ~(i - 1) = (i - 1) * ~1