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Proof step 24 from proof sis-neg-low (previous step)

# int2bits(j0) = 17, j0 < 0, j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 * 65536 + j0 < 0, i0 < 0 ⊦ j0 = 0, s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + fillsgn(16, int2bits(j0).rest))))) = j0 + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 26:
¬ 16 ≤ # int2bits(j0).rest, # int2bits(j0) = 17, j0 < 0, j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 * 65536 + j0 < 0, i0 < 0 ⊦ j0 = 0, s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + fillsgn(16, int2bits(j0).rest))))) = j0 + 65536
Proof step 29:
16 ≤ # int2bits(j0).rest, # int2bits(j0) = 17, j0 < 0, j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 * 65536 + j0 < 0, i0 < 0 ⊦ j0 = 0, s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + int2bits(j0).rest)))) = j0 + 65536

Rule argument

spec: bitopsaux inst: name: fillsgn-longer seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [int2bits(j0).rest, 16] flags: rewrite

Additional information

Used terms: int2bits(j0).rest, 16