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Proof step 8 from proof nummult-ls (previous step)

i + j = (i1 * i + j0) + 1, 0 < i + j, 0 ≤ j0, j0 < i, i1 ≤ i0, 0 ≤ j, 0 < i, i * i0 < j, 0 ≤ i0, 0 ≤ i1 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 9:
j = (i1 - 1) * i + j0 + 1, i + j = (i1 * i + j0) + 1, 0 < i + j, 0 ≤ j0, j0 < i, i1 ≤ i0, 0 ≤ j, 0 < i, i * i0 < j, 0 ≤ i0, 0 ≤ i1 ⊦
Proof step 14:
i + j = (i1 * i + j0) + 1, 0 < i + j, 0 ≤ j0, j0 < i, i1 ≤ i0, 0 ≤ j, 0 < i, i * i0 < j, 0 ≤ i0, 0 ≤ i1 ⊦ j = (i1 - 1) * i + j0 + 1

Rule argument

fma: j = (i1 - 1) * i + j0 + 1

Additional information

Used formulas: j = (i1 - 1) * i + j0 + 1