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Proof step 2 from proof band-011x-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ false ∈ int2bits(j).rest ↔ ¬(∃ i. j = 2 ^ i - 1) subst: [j] → [i] rotate: F spec: int2bits inst: name: int2bits-falsein-02

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i < 0 → 2 ^ i = 0;% ⊦ ¬ i ≤ j ↔ j < i;%0 ≤ i ⊦ int2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i));% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ 0 + m = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ n→i(i→n(i)) = abs(i);% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 ≤ i → abs(i) = i;% ⊦ i + j = i + i0 ↔ j = i0; Used terms: i