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Proof step 55 from proof bitsand-fillsgn (previous step)

∀ n, bits, bits1. # bits1 < #(false + []) → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ n0 = 1, n0 = 0, fillsgn(n0, bitsand(mklist(true, n0), false ')) = mklist(false, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsand(bits, bits0) = false '
Proof step 57:
mklist(true, n0) ≠ [] ∧ false ' = false ', ∀ n, bits, bits1. # bits1 < #(false + []) → true → bits = [] ∨ bits1 = [] ∨ fillsgn(n, bitsand(fillsgn(n, bits), bits1)) = fillsgn(n, bitsand(bits, bits1)) ⊦ n0 = 1, n0 = 0, fillsgn(n0, false ') = mklist(false, n0)

Rule argument

name: and-rec-02 rotate: F subst: [bits0, bits] → [false ', mklist(true, n0)]

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m) = [] ↔ m = 0; Used terms: false ', mklist(true, n0)