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Proof step 65 from proof cast-mod-neg-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i + 1 = 0 → int2bits(i) = true ' subst: [i] → [~1] rotate: F spec: int2bits inst: name: int2bits-mone

Additional information

Used simplifier rules: ⊦ fillsgn(n + 1, boolvar ') = mklist(boolvar, n + 1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);%n ≠ 0 ⊦ mklist(true, (* n)) = true ' + mklist(true, 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;% ⊦ lastn(n, bits + mklist(boolvar, n)) = mklist(boolvar, n);% ⊦ boolvar ' + bits ≠ [];% ⊦ #(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: ~1