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Proof step 19 from proof band-011x-is-lastn (previous step)

# bits = i→n(i) + 1, int2bits(j) = bits0 + bits, i→n(i) < # bits, 0 < i, i→n(i) < # bits0 + # bits ⊦ i→n(i) = # bits0 + # bits, bits = [], bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(bits.rest)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
bits = boolvar + bits1, # bits = i→n(i) + 1, int2bits(j) = bits0 + bits, i→n(i) < # bits, 0 < i, i→n(i) < # bits0 + # bits ⊦ i→n(i) = # bits0 + # bits, bits = [], bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(bits1)

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits, boolvar, bits1] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bits, boolvar, bits1