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Proof step 61 from proof band-011x-pos (previous step)

bits2uint((false ' + bitsinvert(bits0))+1) + (j / 2) % 2 ^ i0 = 0, j % 2 = 1, uint2bits(j / 2) = true ' + bits, bitsand(false ' + mklist(true, i→n(i0)), true ' + bits) = true ' + bits0, 0 < j, 0 ≤ j, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ ~1 = bits2uint(bitsinvert(bits0)) * 2 + j % (2 ^ i0 * 2), j = 1, ~1 = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → uint2bits(i) ≠ true ' + bits subst: [bits, i] → [bits, j / 2] rotate: F spec: int2bits inst: name: uint2bits-first-01

Additional information

Used simplifier rules: ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; Used terms: bits, j / 2