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Proof step 10 from proof modex-odd-neg-01 (previous step)

2 * (i0 + 1) = i + 1, i0 < 0 ⊦ i = 2 * i0 + 1

User applied rule cut formula

And closed the goal!

Rule argument

fma: i = 2 * (i0 + 1) - 1

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ i + (j - i) = j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i * j + i = i * (j + 1); (s) Used formulas: i = 2 * (i0 + 1) - 1