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Proof step 52 from proof int2int-neg (previous step)

0 ≤ i ∧ 0 < 3, 0 ≤ 2 ^ i + 2 ^ i, 0 < i + 2 ^ i, 0 ≤ 2 ^ i + i, 1 < 2 ^ i + 2 ^ i, ~2 ≤ 2 ^ i + i, ~2 < i + 2 ^ i, ~2 < i, 0 ≤ 2 ^ i, 0 ≤ i, ~2 ≤ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (n→i(#(uint2bits(3) + mklist(false, i→n(i)))) - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
0 ≤ 2 ^ i + 2 ^ i, 0 < i + 2 ^ i, 0 ≤ 2 ^ i + i, 1 < 2 ^ i + 2 ^ i, ~2 ≤ 2 ^ i + i, ~2 < i + 2 ^ i, ~2 < i, 0 ≤ 2 ^ i, 0 ≤ i, ~2 ≤ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (2 + i)

Rule argument

Additional information

Used simplifier rules: uint2bits-pos-num: 1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 ≤ i → n→i(i→n(i)) = i;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';