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Proof step 36 from proof sis-neg-high (previous step)

~32768 < j, # int2bits(j) ≤ 16, ~32768 ≤ j, 65536 * i0 + j < ~32768, 65536 * i0 + j < 0, i0 < 0, j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + fillsgn(16, int2bits(j)))))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 38:
16 = # fillsgn(16, int2bits(j)), ~32768 < j, # int2bits(j) ≤ 16, ~32768 ≤ j, 65536 * i0 + j < ~32768, 65536 * i0 + j < 0, i0 < 0, j < 0 ⊦ s2i(i2s(bits2int(fillsgn(16, int2bits(j))))) = j

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [fillsgn(16, int2bits(j)), int2bits(i0 - 1), 16] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used simplifier rules: ⊦ # bits ≤ n → # fillsgn(n, bits) = n; Used terms: fillsgn(16, int2bits(j)), int2bits(i0 - 1), 16