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Proof step 10 from proof sis-on-bits (previous step)

16 < # int2bits(i), ~32768 ≤ i, i ≤ 32767 ⊦ i = bits2int(lastn(16, int2bits(i))), 16 = # fillsgn(16, int2bits(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1))
Proof step 12:
¬ 0 < i, 16 < # int2bits(i), ~32768 ≤ i, i ≤ 32767 ⊦ i = bits2int(lastn(16, int2bits(i))), 16 = # fillsgn(16, int2bits(i))

Rule argument

seq: ⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1)) subst: [i, m] → [i, 16] rotate: F spec: int2bits inst: name: int2bits-lslen-06

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); Used terms: i, 16