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Proof step 30 from proof bytes2bytes-zero (previous step)

b2i(by) = 0, b2i(by0) < 0, # fillsgn(8, int2bits(b2i(by0))) ≤ 7, ∀ by0, by, bytes0. # bytes0 < # [] → b2i(by) = 0 ∧ b2i(by0) < 0 → bits2bytes(sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0))) = by ' + by0 ' + bytes0 ⊦ bits2bytes(false ' + fillsgn(8, int2bits(b2i(by0)))) = by ' + by0 ', fillsgn(8, int2bits(b2i(by0))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ # bits ≤ n → # fillsgn(n, bits) = n

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ 8 < # int2bits(b2i(by)); Used terms: int2bits(b2i(by0)), 8