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Proof step 24 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)) ⊦ bits0 = [], fillsgn(n, bitsand(mklist(false, n), bits0)) = mklist(false, n), n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ ¬ true ∈ bits ∧ (# bits0 < # bits ∧ ¬ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = mklist(false, # bits0)
Proof step 26:
¬(¬ true ∈ mklist(false, n) ∧ # bits0 < # mklist(false, n) ∧ ¬ bits0.first ∧ mklist(false, n) ≠ [] ∧ bits0 ≠ []), ∀ n, bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ bits0 = [], fillsgn(n, bitsand(mklist(false, n), bits0)) = mklist(false, n), n = 0
Proof step 31:
¬ true ∈ mklist(false, n) ∧ # bits0 < # mklist(false, n) ∧ ¬ bits0.first ∧ mklist(false, n) ≠ [] ∧ bits0 ≠ [], ∀ n, bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ bits0 = [], fillsgn(n, mklist(false, # bits0)) = mklist(false, n), n = 0

Rule argument

name: bitsand-zeros-01 rotate: F subst: [bits0, bits] → [bits0, mklist(false, n)]

Additional information

Used terms: bits0, mklist(false, n)