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Proof step 339 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 340:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 341:
# bits ≤ n ∧ bits ≠ [], n = #(mklist(bits.first, n - # bits) + bits), mklist(false, # bits) = bits, # bits0 + 1 < n, # bits < n, # bits0 < # bits, bits0.first, # bits0 < n ⊦ bits0 = [], bits = [], mklist(false, n) = mklist(bits.first, n - # bits) + bits

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [bits, n] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits, n