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Proof step 4 from proof shiftzero-max-neg-01 (previous step)

# int2bits(i) ≤ n, j ≤ n→i(n), 2 ^ (n→i(n) - j) ≤ >>>(n, i, j), i < 0, 0 < j, ∀ n, i, j0. i→n(j0) < i→n(j) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i < ~1 ∧ n < # int2bits(i) ∧ 1 < j → >>>(n, i, j) = >>>(n, (i - 1) / 2, j - 1)
Proof step 6:
¬(i < ~1 ∧ n < # int2bits(i) ∧ 1 < j), # int2bits(i) ≤ n, j ≤ n→i(n), 2 ^ (n→i(n) - j) ≤ >>>(n, i, j), i < 0, 0 < j, ∀ n, i, j0. i→n(j0) < i→n(j) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0

Rule argument

name: shiftzero-rec-neg-longer rotate: F subst: [j, i, n] → [j, i, n]

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); Used terms: j, i, n