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Proof step 24 from proof getShort-isi (previous step)

b2i(byi) < 0 ⊦ s2i(i2s(bor((b2i(byi) + 1) * 256 - 1 + bits2uint(mklist(true, 8)), band(b2i(byj), 255)))) = bor((b2i(byi) + 1) * 256 - 1 + bits2uint(mklist(true, 8)), band(b2i(byj), 255)), ¬ bor((b2i(byi) + 1) * 256 - 1 + bits2uint(mklist(true, 8)), band(b2i(byj), 255)) < ~32768 ∧ ¬ 32767 < bor((b2i(byi) + 1) * 256 - 1 + bits2uint(mklist(true, 8)), band(b2i(byj), 255))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ ¬ false ∈ bits ∧ bits ≠ [] → bits2uint(bits) = 2 ^ n→i(# bits) - 1
Proof step 26:
¬ false ∈ mklist(true, 8) ∧ mklist(true, 8) ≠ [], b2i(byi) < 0 ⊦ s2i(i2s(bor((b2i(byi) + 1) * 256 - 1 + (2 ^ n→i(# mklist(true, 8)) - 1), band(b2i(byj), 255)))) = bor((b2i(byi) + 1) * 256 - 1 + (2 ^ n→i(# mklist(true, 8)) - 1), band(b2i(byj), 255)), ¬ bor((b2i(byi) + 1) * 256 - 1 + (2 ^ n→i(# mklist(true, 8)) - 1), band(b2i(byj), 255)) < ~32768 ∧ ¬ 32767 < bor((b2i(byi) + 1) * 256 - 1 + (2 ^ n→i(# mklist(true, 8)) - 1), band(b2i(byj), 255))

Rule argument

seq: ⊦ ¬ false ∈ bits ∧ bits ≠ [] → bits2uint(bits) = 2 ^ n→i(# bits) - 1 subst: [bits] → [mklist(true, 8)] rotate: F spec: int2bits inst: name: bits2uint-ones

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ false ∈ mklist(true, n);% ⊦ mklist(boolvar, m) = [] ↔ m = 0; Used terms: mklist(true, 8)