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Proof step 71 from proof intshiftrzero-prop-01 (previous step)

2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i))).first, # int2bits(i) ≤ 32, ~2147483648 ≤ i, i < 0, band(j, 31) ≤ 31, 0 < band(j, 31) ⊦ 32 - i→n(band(j, 31)) = 0, band(j, 31) = 0, 2 ^ n→i(32 - 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: ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n) subst: [n, m] → [i→n(band(j, 31)), 32] rotate: F spec: intnat inst: name: n2i-sub

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