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Proof step 29 from proof sis-pos-high (previous step)

# int2bits(j0) = 17, 0 < j0, 0 < i0 * 65536 + j0, 0 ≤ i0, 0 ≤ j0, 32767 < j0, 32767 < i0 * 65536 + j0, j0 < 65536, 0 < i0 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j0)).rest)))) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 31:
16 ≠ # fillsgn(17, int2bits(j0)).rest, # int2bits(j0) = 17, 0 < j0, 0 < i0 * 65536 + j0, 0 ≤ i0, 0 ≤ j0, 32767 < j0, 32767 < i0 * 65536 + j0, j0 < 65536, 0 < i0 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j0)).rest)))) + 65536
Proof step 37:
16 = # fillsgn(17, int2bits(j0)).rest, # int2bits(j0) = 17, 0 < j0, 0 < i0 * 65536 + j0, 0 ≤ i0, 0 ≤ j0, 32767 < j0, 32767 < i0 * 65536 + j0, j0 < 65536, 0 < i0 ⊦ j0 = s2i(i2s(bits2int(fillsgn(17, int2bits(j0)).rest))) + 65536

Rule argument

spec: list-del inst: bitlista name: lastN-append seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [fillsgn(17, int2bits(j0)).rest, int2bits(i0), 16] flags: rewrite

Additional information

Used terms: fillsgn(17, int2bits(j0)).rest, int2bits(i0), 16