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Proof step 39 from proof bytes2bytes-zero (previous step)

8 = # fillsgn(8, int2bits(b2i(by0))), b2i(by) = 0, b2i(by0) < 0, ∀ by0, by, bytes0. # bytes0 < # [] → b2i(by) = 0 ∧ b2i(by0) < 0 → bits2bytes(sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0))) = by ' + by0 ' + bytes0 ⊦ bits2bytes(firstn(1, false ' + fillsgn(8, int2bits(b2i(by0))))) + i2b(bits2int(fillsgn(8, int2bits(b2i(by0))))) ' = by ' + by0 ', fillsgn(8, int2bits(b2i(by0))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits) subst: [bits, n] → [int2bits(b2i(by0)), 8] rotate: F spec: int2bits inst: name: bits2int-fill

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(b2i(by0)), 8