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Proof step 39 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(fillsgn(16, int2bits(j))))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits)
Proof step 41:
int2bits(j) ≠ [], ~32768 < j, # int2bits(j) ≤ 16, ~32768 ≤ j, 65536 * i0 + j < ~32768, 65536 * i0 + j < 0, i0 < 0, j < 0 ⊦ s2i(i2s(bits2int(int2bits(j)))) = j

Rule argument

seq: ⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits) subst: [bits, n] → [int2bits(j), 16] rotate: F spec: int2bits inst: name: bits2int-fill

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j), 16