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Proof step 291 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 292:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 293:
n ≠ # fillsgn(n, bits0), n = # fillsgn(n, bits), # bits = n0 + # bits0, # bits0 < n, # bits < n, true ∈ bits, bits0.first, # bits0 ≤ # bits ⊦ lastn(n, fillsgn(n, bits0)) = lastn(n, fillsgn(n, mklist(true, n0) + bits0)), bits = [], bits0 = [], false ∈ bits
Proof step 296:
n = # fillsgn(n, bits0), n = # fillsgn(n, bits), # bits = n0 + # bits0, # bits0 < n, # bits < n, true ∈ bits, bits0.first, # bits0 ≤ # bits ⊦ fillsgn(n, bits0) = lastn(n, fillsgn(n, mklist(true, n0) + bits0)), bits = [], bits0 = [], false ∈ bits

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [fillsgn(n, bits0), n] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

Used terms: fillsgn(n, bits0), n