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Proof step 344 from proof bitsand-cast (previous step)

mklist(false, # bits) = bits, # bits0 + 1 < n0 + # bits, # bits0 < n0 + # bits, bits0.first, # bits0 < # bits ⊦ bits0 = [], bits = [], n0 = 0, mklist(false, n0) = mklist(bits.first, n0)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 345:
bits0 = boolvar + bits1, mklist(false, # bits) = bits, # bits0 + 1 < n0 + # bits, # bits0 < n0 + # bits, boolvar, # bits0 < # bits ⊦ bits0 = [], bits = [], n0 = 0, mklist(false, n0) = mklist(bits.first, n0)

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits0, boolvar, bits1] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

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