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Proof step 17 from proof uint2bits-len-add (previous step)

0 ≤ i, 0 ≤ j0, 0 < j, j0 < 2 ^ i, i→n(i) + 1 < # int2bits(j0) ⊦ # fillsgn(i→n(i) + 1, int2bits(j0)) - 1 = i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: int2bits-lslen-06 rotate: F subst: [i, m] → [j0, i→n(i) + 1]

Additional information

Used simplifier rules: int2bits-zero: ⊦ int2bits(0) = false ';% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ 0 ≤ i → n→i(i→n(i)) = i;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ fillsgn(n + 1, boolvar ') = mklist(boolvar, n + 1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ mklist(boolvar, 1) = boolvar ';% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ 0 + m = m;% ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j); Used terms: j0, i→n(i) + 1