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Proof step 1030 from proof bitsand-cast (previous step)

# bits1 = # fillsgn(# bits1, mklist(false, # bits0)), # bits0 < # bits1 ⊦ bits1 = [], bits0 = [], bits2 + bits1 = [], bits1 = fillsgn(# bits1, mklist(false, # bits0)), true ∈ bits1, bits0.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1031:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 1032:
# mklist(false, # bits0) ≤ # bits1 ∧ mklist(false, # bits0) ≠ [], # bits1 = #(mklist(mklist(false, # bits0).first, # bits1 - # mklist(false, # bits0)) + mklist(false, # bits0)), # bits0 < # bits1 ⊦ bits1 = [], bits0 = [], bits2 + bits1 = [], bits1 = mklist(mklist(false, # bits0).first, # bits1 - # mklist(false, # bits0)) + mklist(false, # bits0), true ∈ bits1, bits0.first

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [mklist(false, # bits0), # bits1] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ # bits = 0 ↔ bits = []; Used terms: mklist(false, # bits0), # bits1