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Proof step 6 from proof band-min (previous step)

# int2bits(i) = # int2bits(j), i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, j ≤ 0, i ≤ 0, bits2int(bitsand(int2bits(i), int2bits(j))) < i0, ∀ i0, j, i1. i→n(i1) < i→n(i) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'
Proof step 8:
¬(i < 0 ∧ i ≠ ~1), # int2bits(i) = # int2bits(j), i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, j ≤ 0, i ≤ 0, bits2int(bitsand(int2bits(i), int2bits(j))) < i0, ∀ i0, j, i1. i→n(i1) < i→n(i) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦
Proof step 27:
i < 0 ∧ i ≠ ~1, #(int2bits((i - 1) / 2) + (~1 = i % 2)') = # int2bits(j), i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, j ≤ 0, i ≤ 0, bits2int(bitsand(int2bits((i - 1) / 2) + (~1 = i % 2)', int2bits(j))) < i0, ∀ i0, j, i1. i→n(i1) < i→n(i) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦

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 terms: i