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Proof step 58 from proof cast-mod-pos-high (previous step)

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

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) - 1)) subst: [m, i] → [i→n(i), j % 2 ^ i] rotate: F spec: int2bits inst: name: int2bits-lelen

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ j ∧ 0 < i → (j % 2 ^ i ≤ 0 ↔ j % 2 ^ i = 0);% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ int2bits(0) = false ';% ⊦ fillsgn(n + 1, boolvar ') = mklist(boolvar, n + 1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ # mklist(boolvar, n) = n;% ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j);% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 2 ^ i ≤ 0 ↔ i < 0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i→n(i), j % 2 ^ i