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Proof step 38 from proof band-min (previous step)

# int2bits(i2 / 2) = # int2bits(i / 2), bits2int(bitsand(int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)', int2bits(i / 2) + (~1 = (i + 1) % 2)')) < i0, i2 < ~1, i2 < 0, i < ~1, 2 ^ (n→i(# int2bits(i / 2)) + 1) + i0 ≤ 0, i < 0, ∀ i0, j, i1. i→n(i1) < i→n(i2 + 1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦ ~2 = i2, ~2 = i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [int2bits(i / 2) + (~1 = (i + 1) % 2)', int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)']

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: int2bits(i / 2) + (~1 = (i + 1) % 2)', int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)'