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Proof step 1 from proof add-ones-grlen-01 (conclusion)

⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits0, bits) = fillsgn(# bits, bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 3:
bits0 ≠ [] ∧ bits ≠ [] ⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits, bits0]

Additional information

Used simplifier rules: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits;% ⊦ # [] = 0;% ⊦ m ≤ 0 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = []; Used terms: bits, bits0