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Proof step 21 from proof bits2int-le8 (previous step)

# sgn(bits) = 2 + i→n(i), bits2int(bits) < 64, 2 ^ i ≤ 64, bits2int(bits) < 0, bits2int(bits) < ~1, bits2int(bits) + 2 ^ i < i, bits2int(bits) < ~128, # bits ≤ 8, bits2int(bits) + 2 ^ i < 0, 0 ≤ i, 0 ≤ bits2int(bits) + 2 ^ i * 2, bits2int(bits) + 1 < 2 ^ i * 2, bits2int(bits) < 2 ^ i * 2, bits2int(bits) + 1 < 2 ^ i, 0 < 2 ^ i, bits2int(bits) < 2 ^ i, bits2int(bits) < i, bits2int(bits) < 63 ⊦ i = ~1, bits = []

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: i ≤ j + i0, j < j0 ⊦ i < j0 + i0 subst: [i, j, i0, j0] → [0, bits2int(bits), 2 ^ i * 2, ~128] rotate: F spec: int-abs inst: name: pls-01

Additional information

Used simplifier rules: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 0, bits2int(bits), 2 ^ i * 2, ~128