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Proof step 9 from proof bitsor-mklist-in (previous step)

# bits0 = 1, ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < 1 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits0) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits0), bits0 = [], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsor(bits, bits0) = true '
Proof step 11:
¬(mklist(boolvar0, n) + bits ≠ [] ∧ bits0 = true '), # bits0 = 1, ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < 1 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits0) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits0), bits0 = [], n = 0
Proof step 17:
mklist(boolvar0, n) + bits ≠ [] ∧ bits0 = true ', # bits0 = 1, ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < 1 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ boolvar ∈ true ' ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits0), bits0 = [], n = 0

Rule argument

name: or-rec-01 rotate: F subst: [bits0, bits] → [bits0, mklist(boolvar0, n) + bits]

Additional information

Used terms: bits0, mklist(boolvar0, n) + bits