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Proof step 9 from proof intshiftrzero-prop-01 (previous step)

~2147483648 ≤ i, i < 0 ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = bits2int(int2bits(2) + mklist(false, i→n(band(~(j + 1), 31)))) + (i i>> j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(~ j, i) = band(i + 1 - j, i)
Proof step 11:
¬(¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31), ~2147483648 ≤ i, i < 0 ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = bits2int(int2bits(2) + mklist(false, i→n(band(~(j + 1), 31)))) + (i i>> j)
Proof step 16:
¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31, ~2147483648 ≤ i, i < 0 ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = bits2int(int2bits(2) + mklist(false, i→n(band(31 + 1 - j + 1, 31)))) + (i i>> j)

Rule argument

name: band-011x-neg-03 rotate: F subst: [i, j] → [31, j + 1]

Additional information

Used terms: 31, j + 1