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Proof step 20 from proof sis-pos-low (previous step)

32767 < 65536 * i0 + j, j ≤ 32767, 0 < 65536 * i0 + j, 0 ≤ j, 0 ≤ i0, 0 < i0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j)).rest)))) = j, fillsgn(17, int2bits(j)) = [], 16 = # fillsgn(17, int2bits(j)) - 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 22:
¬ # int2bits(j) ≤ 17, 32767 < 65536 * i0 + j, j ≤ 32767, 0 < 65536 * i0 + j, 0 ≤ j, 0 ≤ i0, 0 < i0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j)).rest)))) = j, fillsgn(17, int2bits(j)) = [], 16 = # fillsgn(17, int2bits(j)) - 1

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [int2bits(j), 17] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: int2bits(j), 17