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Proof step 18 from proof uint2bits-falsein-01 (previous step)

false ∈ uint2bits(i0).rest ↔ (∀ i. 2 ^ i ≠ i0 + 1), 0 < i0, ∀ j0. i→n(j0) < i→n(i0 * 2 + 1) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ false ∈ uint2bits(i0).rest ↔ (∀ i. 2 ^ i ≠ 2 * (i0 + 1)), i0 = 0

User applied rule case distinction

And obtained the following new goals

Proof step 19:
false ∈ uint2bits(i0).rest, false ∈ uint2bits(i0).rest ↔ (∀ i. 2 ^ i ≠ i0 + 1), 0 < i0, ∀ j0. i→n(j0) < i→n(i0 * 2 + 1) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ ∀ i. 2 ^ i ≠ 2 * (i0 + 1), i0 = 0
Proof step 27:
∀ i. 2 ^ i ≠ 2 * (i0 + 1), false ∈ uint2bits(i0).rest ↔ (∀ i. 2 ^ i ≠ i0 + 1), 0 < i0, ∀ j0. i→n(j0) < i→n(i0 * 2 + 1) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ false ∈ uint2bits(i0).rest, i0 = 0

Rule argument

pos: right 1

Proof step 18 from proof uint2bits-falsein-01 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information