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Proof step 19 from proof intshiftrsign-if (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits ≠ [] ∧ (bits.first ↔ boolvar) → bits2int(mklist(boolvar, n) + bits) = bits2int(bits)
Proof step 21:
¬(sublist(0, n, int2bits(i)) ≠ [] ∧ (sublist(0, n, int2bits(i)).first ↔ ¬ 0 ≤ i)), # int2bits(i) = n + i→n(band(j, 31)), i→n(band(j, 31)) < # int2bits(i) ⊦ bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, n, int2bits(i))) = bits2int(sublist(0, n, int2bits(i))), n = 0

Rule argument

seq: ⊦ bits ≠ [] ∧ (bits.first ↔ boolvar) → bits2int(mklist(boolvar, n) + bits) = bits2int(bits) subst: [bits, n, boolvar] → [sublist(0, n, int2bits(i)), i→n(band(j, 31)), ¬ 0 ≤ i] rotate: F spec: int2bits inst: name: bits2int-mklist

Additional information

Used terms: sublist(0, n, int2bits(i)), i→n(band(j, 31)), ¬ 0 ≤ i