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Proof step 2 from proof uint2bits-falsein-01 (previous step)

0 < j ⊦ false ∈ uint2bits(j).rest ↔ (∀ i. 2 ^ i ≠ j + 1)

User applied rule induction

And obtained the following new goals

Proof step 3:
0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ false ∈ uint2bits(j).rest ↔ (∀ i. 2 ^ i ≠ j + 1)

Rule argument

indvar: i→n(j) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j)