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Proof step 46 from proof sis-on-bits (previous step)

16 ≤ # int2bits(i) ⊦ ¬ bits2int(lastn(16, int2bits(i))) < ~32768, s2i(i2s(bits2int(lastn(16, int2bits(i))))) = bits2int(lastn(16, int2bits(i))), ¬ i < ~32768 ∧ ¬ 32767 < i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
bits2int(lastn(16, int2bits(i))) < ~32768, 16 ≤ # int2bits(i), bits2int(lastn(16, int2bits(i))) < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = bits2int(lastn(16, int2bits(i))), ¬ i < ~32768 ∧ ¬ 32767 < i

Rule argument

Additional information

Used simplifier rules: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)