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Proof step 11 from proof uint2bits-falsein-01 (previous step)

j % 2 = 0, 2 ^ i = j + 1, 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ j = 1

User applied rule cut formula

And obtained the following new goals

Proof step 12:
j = 2 ^ i - 1, j % 2 = 0, 2 ^ i = j + 1, 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ j = 1

Rule argument

fma: j = 2 ^ i - 1

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; Used formulas: j = 2 ^ i - 1