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Proof step 36 from proof intshiftrzero-prop-01 (previous step)

¬ # int2bits(i) ≤ 32, 2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), ~2147483648 ≤ i, i < 0, band(j, 31) ≤ 31, 0 < 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 ^ (32 - band(j, 31)), false ∈ int2bits(31).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), 32 < # int2bits(i), 0 < band(j, 31), band(j, 31) ≤ 31, i < 0, ~2147483648 ≤ i ⊦ bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = (i i>> j) + 2 ^ (32 - band(j, 31)), band(j, 31) = 0, false ∈ int2bits(31).rest

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ ¬ m ≤ n ↔ n < m;