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Proof step 12 from proof mod-zero-one (previous step)

i0 % j + i % j < 2 * j, 0 ≤ i, 0 ≤ i0, 0 < j, 1 < (i % j + i0 % j) / j, 0 < (i % j + i0 % j) / j ⊦ (i % j + i0 % j) / j = 1

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: (i % j + i0 % j) / j < (2 * j) / j

Additional information

Used simplifier rules: div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1 Used formulas: (i % j + i0 % j) / j < (2 * j) / j