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Proof step 18 from proof cast-mod-pos-high (previous step)

0 ≤ i, i→n(i) ≤ # int2bits(j), 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j, 2 ^ (i - 1) ≤ j, 0 ≤ 2 ^ (i - 1) + j, j < 2 ^ i ⊦ # int2bits(j) = i→n(i) + 1, j % 2 ^ i = bits2int(lastn(i→n(i), int2bits(j))) + 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ 0 ≤ j → 2 ^ j ≠ 0;%j ≠ 0 ⊦ 0 % j = 0;% ⊦ int2bits(0) = false ';% ⊦ # boolvar ' = 0 +1;% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 2 ^ i ≤ 0 ↔ i < 0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ 0 ≤ i → (i < 1 ↔ i = 0); Used terms: j, i→n(i)