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Proof step 10 from proof mod-nls-04 (previous step)

i0 + j = 1, i % j < i0, i0 < 0, i0 < j, i0 + 1 < j, i % j < 0, i % j < ~1, 0 < j + i % j, i0 + 1 < j + i % j, i0 < j + i % j, 1 < j, 0 < j ⊦

User applied rule cut formula

And closed the goal!

Rule argument

fma: i0 = ~(j - 1)

Additional information

Used simplifier rules: mod-lezero: ⊦ 0 < j → ¬ j + i % j ≤ 0;%minus-02: ⊦ ~(i - 1) = ~ i + 1; from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs Used formulas: i0 = ~(j - 1)