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Proof step 20 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)))) = (i i>> j) + bits2int(int2bits(2) + mklist(false, i→n(31 - band(j, 31)))), false ∈ int2bits(31).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j) subst: [j, i] → [band(j, 31), 31] rotate: F spec: intnat inst: name: sub

Additional information

Used simplifier rules: band-max-02: ⊦ 0 ≤ i ∧ i ≤ i0 → ¬ i0 < band(i, j);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);%band-ls-zero-01: ⊦ ¬ band(j, 31) < 0;% ⊦ ¬ i ≤ j ↔ j < i; Used terms: band(j, 31), 31