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Proof step 51 from proof shiftzero-max-neg (previous step)

# int2bits(i) ≤ # int2bits((i - 1) / 2), m < # int2bits((i - 1) / 2), 2 ^ n→i(m) ≤ >>>(m, (i - 1) / 2, j - 1), # int2bits(i) ≤ m + 1, i < ~1, i < 0, 0 < j, 1 < j, ∀ n, i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ # int2bits(i) ≤ n ∧ 0 < j0 ∧ n ≠ 0 → >>>(n, i, j0) < 2 ^ (n→i(n) - 1) ⊦ j = 1, m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'

Rule argument

seq: ⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)' subst: [j] → [i] rotate: F spec: int2bits inst: name: int2bits-rec-neg

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + m0 ≤ m ↔ m0 = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i