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Proof step 9 from proof int2bits-lslen-08 (previous step)

j < 0 → (∃ i. ~1 ≤ i ∧ j < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ j), # int2bits(j) + 1 < # int2bits(j - 1), j < 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# int2bits(j) + 1 < # int2bits(j - 1), j < 0, ~1 ≤ i, j + 2 ^ i < 0, 0 ≤ 2 ^ (i + 1) + j ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;