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Proof step 8 from proof num-i2l-pos (previous step)

0 < i, 9223372036854775807 < i, # int2bits(i) ≤ 64 ⊦ i2l(cast(64, i)) = i2l(bits2int(lastn(64, int2bits(i))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < i → (# int2bits(i) ≤ m ↔ i < 2 ^ (n→i(m) - 1))

Rule argument

seq: ⊦ 0 < i → (# int2bits(i) ≤ m ↔ i < 2 ^ (n→i(m) - 1)) subst: [m, i] → [64, i] rotate: F spec: int2bits inst: name: int2bits-lelen

Additional information

Used simplifier rules: i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: 64, i