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Proof step 14 from proof bits2int-le8 (previous step)

~(2 ^ (i + 1)) < ~(2 ^ 7), # sgn(bits) = 2 + i→n(i), bits2int(bits) < i, bits2int(bits) < 2 ^ i, 0 < 2 ^ i, bits2int(bits) + 1 < 2 ^ i, bits2int(bits) < 2 ^ i * 2, bits2int(bits) + 1 < 2 ^ i * 2, 0 ≤ bits2int(bits) + 2 ^ i * 2, 0 ≤ i, bits2int(bits) + 2 ^ i < 0, # bits ≤ 8, bits2int(bits) < ~128, bits2int(bits) + 2 ^ i < i, bits2int(bits) < ~1, bits2int(bits) < 0 ⊦ bits = [], i = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ~ j < ~ i ↔ i < j
Proof step 16:
2 ^ 7 < 2 ^ (i + 1), # sgn(bits) = 2 + i→n(i), bits2int(bits) < i, bits2int(bits) < 2 ^ i, 0 < 2 ^ i, bits2int(bits) + 1 < 2 ^ i, bits2int(bits) < 2 ^ i * 2, bits2int(bits) + 1 < 2 ^ i * 2, 0 ≤ bits2int(bits) + 2 ^ i * 2, 0 ≤ i, bits2int(bits) + 2 ^ i < 0, # bits ≤ 8, bits2int(bits) < ~128, bits2int(bits) + 2 ^ i < i, bits2int(bits) < ~1, bits2int(bits) < 0 ⊦ bits = [], i = ~1

Rule argument

seq: ⊦ ~ j < ~ i ↔ i < j subst: [i, j] → [2 ^ 7, 2 ^ (i + 1)] rotate: F spec: int-abs inst: name: neg-01

Additional information

Used terms: 2 ^ 7, 2 ^ (i + 1)