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Proof step 37 from proof bib-neg-low (previous step)

8 < # int2bits(j).rest, j < ~128, 256 * i0 + j < ~128, ~256 < j, j < 0, 256 * i0 + j < 0, i0 < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j, 8 = # fillsgn(8, int2bits(j).rest), int2bits(j).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ bits ≠ [] → # bits.rest = (# bits)-1
Proof step 39:
int2bits(j) ≠ [], 8 < (# int2bits(j))-1, j < ~128, 256 * i0 + j < ~128, ~256 < j, j < 0, 256 * i0 + j < 0, i0 < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j, 8 = # fillsgn(8, int2bits(j).rest), int2bits(j).rest = []

Rule argument

seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [int2bits(j)] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j)