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Proof step 19 from proof int2bits-lslen-08 (previous step)

i→n(i + 2) + 1 < # int2bits(~(2 ^ i * 2 + 1)), 0 ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2)
Proof step 21:
¬(0 ≤ i + 1 ∧ ~(2 ^ ((i + 1) + 1)) ≤ ~(2 ^ i * 2 + 1) ∧ ~(2 ^ i * 2 + 1) < ~(2 ^ (i + 1))), i→n(i + 2) + 1 < # int2bits(~(2 ^ i * 2 + 1)), 0 ≤ i ⊦
Proof step 24:
0 ≤ i + 1 ∧ ~(2 ^ ((i + 1) + 1)) ≤ ~(2 ^ i * 2 + 1) ∧ ~(2 ^ i * 2 + 1) < ~(2 ^ (i + 1)), i→n(i + 2) + 1 < i→n((i + 1) + 2), 0 ≤ i ⊦

Rule argument

name: int2bits-len-neg rotate: F subst: [i, j] → [i + 1, ~(2 ^ i * 2 + 1)]

Additional information

Used terms: i + 1, ~(2 ^ i * 2 + 1)