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Proof step 13 from proof add-eq2pot (previous step)

(i2 + 1) * 2 ^ i0 = 2 ^ i0 + j, 2 ^ i1 = i2 + 1, 0 ≤ i0, 0 ≤ j, 0 ≤ i1 + i0, 0 ≤ i1 ⊦ j = 2 ^ i0 * i2

User applied rule cut formula

And obtained the following new goals

Proof step 14:
(i2 + 1) * 2 ^ i0 = 2 ^ i0 + j, 2 ^ i1 = i2 + 1, 0 ≤ i1, 0 ≤ i1 + i0, 0 ≤ j, 0 ≤ i0 ⊦ (i2 + 1) * 2 ^ i0 - 2 ^ i0 = j, j = 2 ^ i0 * i2

Rule argument

fma: (i2 + 1) * 2 ^ i0 - 2 ^ i0 = j

Additional information

Used simplifier rules: ⊦ i * j - i = i * (j - 1); (s)% ⊦ (* i) + i0 - (* j) = (i - j) + i0; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%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: (i2 + 1) * 2 ^ i0 - 2 ^ i0 = j