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Proof step 42 from proof bitsand-fillsgn (previous step)

∀ n, bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ fillsgn(n, bitsand(mklist(true, n), bits0)) = fillsgn(n, bits0), bits0 = [], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 44:
¬(¬ false ∈ mklist(true, n) ∧ # bits0 ≤ # mklist(true, n) ∧ bits0.first ∧ bits0 ≠ []), ∀ n, bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ fillsgn(n, bitsand(mklist(true, n), bits0)) = fillsgn(n, bits0), bits0 = [], n = 0

Rule argument

name: add-ones-grlen rotate: F subst: [bits0, bits] → [bits0, mklist(true, n)]

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ bits ≠ [] → fillsgn(n, fillsgn(n, bits)) = fillsgn(n, bits); Used terms: bits0, mklist(true, n)