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Proof step 14 from proof sis-pos-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 16:
16 ≠ # fillsgn(17, int2bits(j)).rest, 0 < i0, 0 ≤ i0, 0 ≤ j, 0 < 65536 * i0 + j, j ≤ 32767, 32767 < 65536 * i0 + j ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j)).rest)))) = j
Proof step 25:
16 = # fillsgn(17, int2bits(j)).rest, 0 < i0, 0 ≤ i0, 0 ≤ j, 0 < 65536 * i0 + j, j ≤ 32767, 32767 < 65536 * i0 + j ⊦ s2i(i2s(bits2int(fillsgn(17, int2bits(j)).rest))) = j

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [fillsgn(17, int2bits(j)).rest, int2bits(i0), 16] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used terms: fillsgn(17, int2bits(j)).rest, int2bits(i0), 16