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Proof step 12 from proof int2bits-lslen-07 (previous step)

j < 0, j + 2 ^ i < 0, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, 3 + i→n(i) < # int2bits(j + 1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2)
Proof step 14:
¬(0 ≤ i ∧ ~(2 ^ (i + 1)) ≤ j + 1 ∧ j + 1 < ~(2 ^ i)), j < 0, j + 2 ^ i < 0, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, 3 + i→n(i) < # int2bits(j + 1) ⊦
Proof step 16:
0 ≤ i ∧ ~(2 ^ (i + 1)) ≤ j + 1 ∧ j + 1 < ~(2 ^ i), j < 0, j + 2 ^ i < 0, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, 3 + i→n(i) < i→n(i + 2) ⊦

Rule argument

name: int2bits-len-neg rotate: F subst: [i, j] → [i, j + 1]

Additional information

Used terms: i, j + 1