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Proof step 4 from proof uint2bits-len-mon (previous step)

0 ≤ i, i ≤ j, # uint2bits(j) < # uint2bits(i), 0 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ # uint2bits(j0) < # uint2bits(i) ∧ i ≤ j0 ∧ 0 ≤ i → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 6:
¬(0 < j ∧ j ≠ 1), 0 ≤ i, i ≤ j, # uint2bits(j) < # uint2bits(i), 0 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ # uint2bits(j0) < # uint2bits(i) ∧ i ≤ j0 ∧ 0 ≤ i → false ⊦
Proof step 8:
0 < j ∧ j ≠ 1, 0 ≤ i, i ≤ j, #(uint2bits(j / 2) + (j % 2 = 1)) < # uint2bits(i), 0 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ # uint2bits(j0) < # uint2bits(i) ∧ i ≤ j0 ∧ 0 ≤ i → false ⊦

Rule argument

name: uint2bits-rec-01 rotate: F subst: [i] → [j]

Additional information

Used terms: j