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Proof step 37 from proof intshiftrsign32 (previous step)

0 + n0 ≤ # mklist(¬ 0 ≤ i, n1), 32 = n1 + # int2bits(i), 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ band(j, 31) = 0, bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n0, mklist(¬ 0 ≤ i, n1)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: a: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; from specification list[bitlista]%bits2int-mklist-02: ⊦ bits2int(boolvar ' + mklist(boolvar, n)) = bits2int(boolvar '); from specification int2bits%sublist-mklist-02: ⊦ m ≤ m0 → sublist(0, m, mklist(boolvar, m0)) = mklist(boolvar, m); from specification list-del[bitlista]%mk-len: ⊦ # mklist(boolvar, n) = n; from specification list-last[bitlista]%ax-08: ⊦ n + 0 = n; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2