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Proof step 10 from proof cast-mod-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ 2 ^ i ≤ 0 ↔ i < 0;% ⊦ lastn(n, mklist(boolvar, n)) = mklist(boolvar, n);% ⊦ 0 < i → fillsgn(i→n(i), boolvar ') = mklist(boolvar, i→n(i));% ⊦ int2bits(0) = false ';%j ≠ 0 ⊦ 0 % j = 0;% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 < 2 ^ i ↔ 0 < i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 1 ≤ i ↔ 0 < i;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + j < j ↔ i < 0; Used terms: i→n(i), j