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Proof step 19 from proof long-is-cast (previous step)

i < 0, i < ~9223372036854775808, # int2bits(i) ≤ 64 ⊦ l2i(i2l(bits2int(lastn(64, int2bits(i))))) = cast(64, i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ i < ~1 → (# int2bits(i) ≤ m ↔ 0 ≤ i + 2 ^ (n→i(m) - 1))

Rule argument

seq: ⊦ i < ~1 → (# int2bits(i) ≤ m ↔ 0 ≤ i + 2 ^ (n→i(m) - 1)) subst: [m, i] → [64, i] rotate: F spec: int2bits inst: name: int2bits-lelen-03

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 64, i