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Proof step 28 from proof sis-pos-low (previous step)

16 = # int2bits(j).rest, 17 ≤ # int2bits(j), 32767 < 65536 * i0 + j, j ≤ 32767, 0 < 65536 * i0 + j, 0 ≤ j, 0 ≤ i0, 0 < i0 ⊦ s2i(i2s(bits2int(int2bits(j).rest))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ 0 < i → (m ≤ # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 2))

Rule argument

seq: ⊦ 0 < i → (m ≤ # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 2)) subst: [i, m] → [j, 17] rotate: F spec: int2bits inst: name: int2bits-lelen-06

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ int2bits(0) = false ';% ⊦ boolvar '.rest = [];% ⊦ # [] = 0; Used terms: j, 17