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Proof step 304 from proof bitsand-cast (previous step)

n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist((mklist(true, n0) + bits0).first, n1 - n0) + mklist(true, n0) + bits0), false ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 305:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)
Proof step 306:
¬ mklist(true, n0) ≠ [], n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist((mklist(true, n0) + bits0).first, n1 - n0) + mklist(true, n0) + bits0), false ∈ bits
Proof step 309:
mklist(true, n0) ≠ [], n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist(mklist(true, n0).first, n1 - n0) + mklist(true, n0) + bits0), false ∈ bits

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [bits0, mklist(true, n0)] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used terms: bits0, mklist(true, n0)