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Proof step 14 from proof mod-mult-law (previous step)

i - j * j0 = i |%| j, i0 - j * j1 = i0 |%| j, 0 < j ⊦ (i * i0) |%| j = ((i - j * j0) * (i0 - j * j1)) |%| j, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ (i * i0) |%| j = ((i - j * j0) * (i0 - j * j1)) |%| j, j = 0

Rule argument

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs