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Proof step 42 from proof sis-on-bits (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i
Proof step 44:
¬(~32768 ≤ bits2int(lastn(16, int2bits(i))) ∧ bits2int(lastn(16, int2bits(i))) ≤ 32767), 16 ≤ # int2bits(i) ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = bits2int(lastn(16, int2bits(i))), ¬ i < ~32768 ∧ ¬ 32767 < i

Rule argument

name: num-issi rotate: F subst: [i] → [bits2int(lastn(16, int2bits(i)))]

Additional information

Used terms: bits2int(lastn(16, int2bits(i)))