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Proof step 1 from proof cast-law-sub-one-01 (conclusion)

0 < i ⊦ cast(i, j - j0) = cast(i, j - cast(i, j0))

User applied rule cut formula

And obtained the following new goals

Proof step 2:
j - j0 = ~(j0 + ~ j), 0 < i ⊦ cast(i, j - j0) = cast(i, j - cast(i, j0))

Rule argument

fma: j - j0 = ~(j0 + ~ j)

Additional information

Used simplifier rules: ⊦ i + ~ j = i - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ~(i - j) = j - i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j; Used formulas: j - j0 = ~(j0 + ~ j)