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Proof step 44 from proof cast-mod-pos-low (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

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