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Proof step 5 from proof mod-rec-01 (previous step)

i % j + (j - i) % j = 0, i ≤ j, i < 0, j < 0 ⊦ i % j = (i - j) % j

User applied rule cut formula

And obtained the following new goals

Proof step 6:
i % j = ~((j - i) % j), i % j + (j - i) % j = 0, i ≤ j, i < 0, j < 0 ⊦ i % j = (i - j) % j

Rule argument

fma: i % j = ~((j - i) % j)

Additional information

Used simplifier rules: negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: i % j = ~((j - i) % j)