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Proof step 57 from proof intshiftrzero-prop-01 (previous step)

2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), 32 - i→n(band(j, 31)) = 0, 0 < band(j, 31), band(j, 31) ≤ 31, i < 0, ~2147483648 ≤ i, # int2bits(i) ≤ 32 ⊦ band(j, 31) = 0, bits2int(mklist(false, i→n(band(j, 31)))) = bits2int(mklist(true, i→n(band(j, 31)))) + 2 ^ (32 - band(j, 31)), false ∈ int2bits(31).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m ≤ n → (n - m = 0 ↔ n = m) subst: [m, n] → [i→n(band(j, 31)), 32] rotate: F spec: nat inst: name: zero-02

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-ls-zero-01: ⊦ ¬ band(j, 31) < 0;%band-commutativity: ⊦ band(i, j) = band(j, i);%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);%0 ≤ i ⊦ i→n(i) ≤ (* m) ↔ i ≤ n→i(m);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m);% ⊦ i = j → i - j = 0;% ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = j;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i→n(band(j, 31)), 32