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Proof step 21 from proof bytes2bytes-other (previous step)

∀ bytes1. # bytes1 < #([] + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ bits2bytes(sgn(fillsgn(8, int2bits(b2i(by))))) = by ', b2i(by) = ~1, b2i(by) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ bits ≠ [] → sgn(fillsgn(n, bits)) = sgn(bits)
Proof step 23:
int2bits(b2i(by)) ≠ [], ∀ bytes1. # bytes1 < #([] + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ bits2bytes(sgn(int2bits(b2i(by)))) = by ', b2i(by) = ~1, b2i(by) = 0

Rule argument

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

Additional information

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