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Proof step 100 from proof band-min (previous step)

# int2bits(i3) = # int2bits(i2), 2 ^ (n→i(# int2bits(i2)) + 1) + i * 2 + j2 ≤ 0, i2 < i + 2 ^ n→i(# int2bits(i2)), j1 < i + 2 ^ n→i(# int2bits(i2)), i3 < i + 2 ^ n→i(# int2bits(i2)), j0 < i + 2 ^ n→i(# int2bits(i2)), i * 2 + j2 < 0, bits2int(bitsand(int2bits(i3), int2bits(i2))) < 0, i ≤ 0, j2 < i + 2 ^ n→i(# int2bits(i2)), j2 ≤ 0, 0 < i + 2 ^ n→i(# int2bits(i2)), i2 * 2 + j1 < 0, i2 ≤ 0, j1 ≤ 0, i3 * 2 + j0 < 0, i3 ≤ 0, j0 ≤ 0, bits2int(bitsand(int2bits(i3), int2bits(i2))) < i, i2 * 2 + j1 < ~1, i3 * 2 + j0 < ~1, abs(j0) < 2, abs(j1) < 2, abs(j2) < 2, i + 2 ^ (n→i(# int2bits(i2)) + 1) + j2 < 2 ^ n→i(# int2bits(i2)), ∀ i0, j, i1. i→n(i1) < i→n((i3 * 2 + j0) + 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 + j1, ~2 = i3 * 2 + j0, ~1 = ((i3 * 2 + j0) + 1) % 2 ∧ ~1 = ((i2 * 2 + j1) + 1) % 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [n→i(# int2bits(i2)), 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n);% ⊦ i * j + i * j0 = i * (j + j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i ∧ abs(j0) < j → ¬ i * j + j0 ≤ 0; Used terms: n→i(# int2bits(i2)), 2