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Proof step 288 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 289:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 290:
¬ n ≤ # bits0, # bits = n0 + # bits0, n = # fillsgn(n, bits), # bits0 ≤ # bits, bits0.first, true ∈ bits, # bits < n, # bits0 < n ⊦ bits0 = [], bits = [], lastn(n, fillsgn(n, bits0)) = lastn(n, fillsgn(n, mklist(true, n0) + bits0)), false ∈ bits

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bits0, n] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false); Used terms: bits0, n