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Proof step 120 from proof bits2bits-sgn (previous step)

lastn(8, bits) ≠ [] ∧ (lastn(8, bits).first ↔ ¬ true), ¬ false ∈ firstn(# bits - 8, bits) ∧ firstn(# bits - 8, bits) ≠ [], firstn(# bits - 8, bits) + lastn(8, bits) = bits, bits2int(lastn(8, bits)) ≤ 127, 8 < # bits, 0 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], true ' + byte2bits(i2b(bits2int(lastn(8, bits)))) = true ' + lastn(8, bits), false ∈ firstn(# bits - 8, bits), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 121:
⊦ boolvar ' + bits = boolvar ' + bits0 ↔ bits = bits0
Proof step 122:
lastn(8, bits) ≠ [] ∧ (lastn(8, bits).first ↔ ¬ true), ¬ false ∈ firstn(# bits - 8, bits) ∧ firstn(# bits - 8, bits) ≠ [], firstn(# bits - 8, bits) + lastn(8, bits) = bits, bits2int(lastn(8, bits)) ≤ 127, 8 < # bits, 0 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], byte2bits(i2b(bits2int(lastn(8, bits)))) = lastn(8, bits), false ∈ firstn(# bits - 8, bits), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits)))

Rule argument

seq: ⊦ boolvar ' + bits = boolvar ' + bits0 ↔ bits = bits0 subst: [bits0, bits, boolvar] → [lastn(8, bits), byte2bits(i2b(bits2int(lastn(8, bits)))), true] rotate: F spec: list inst: bitlista name: app-08

Additional information

Used terms: lastn(8, bits), byte2bits(i2b(bits2int(lastn(8, bits)))), true