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Proof step 356 from proof bitsand-cast (previous step)

n = # fillsgn(n, bits), # bits0 + 1 < n, # bits0 < # bits, # bits < n, # bits0 < n ⊦ bits0 = [], bits = [], mklist(false, n) = mklist(mklist(false, # bits0).first, n - # bits0) + mklist(false, # bits0), bits0.first, true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 357:
⊦ m ≠ 0 → (mklist(boolvar, m).first ↔ boolvar)
Proof step 358:
# bits0 ≠ 0, n = # fillsgn(n, bits), # bits0 + 1 < n, # bits0 < # bits, # bits < n, # bits0 < n ⊦ bits0 = [], bits = [], mklist(false, n) = mklist(false, n - # bits0) + mklist(false, # bits0), bits0.first, true ∈ bits

Rule argument

seq: ⊦ m ≠ 0 → (mklist(boolvar, m).first ↔ boolvar) subst: [m, boolvar] → [# bits0, false] rotate: F spec: list-last inst: bitlista name: mk-first-01

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = []; Used terms: # bits0, false