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Proof step 73 from proof intshiftrzero-prop-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [32 - band(j, 31), 2] rotate: F spec: int-pot inst: name: Pot-pos

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-commutativity: ⊦ band(i, j) = band(j, i);%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ i + 0 = i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i -1 = i - 1;% ⊦ i - i1 - j = i - i1 + j;% ⊦ (* i) - j + (* i0) = i - i0 - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 32 - band(j, 31), 2