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Proof step 4 from proof bitsor-mklist-in (previous step)

∀ bits, boolvar0, boolvar, n, bits1. # bits1 < # bits0 → 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 5:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsor(bits, bits0) = bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last)
Proof step 6:
¬(1 < #(mklist(boolvar0, n) + bits) ∧ 1 < # bits0), ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < # bits0 → 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 20:
1 < #(mklist(boolvar0, n) + bits) ∧ 1 < # bits0, ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < # bits0 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ boolvar ∈ bitsor((mklist(boolvar0, n) + bits).butlast, bits0.butlast) + ((mklist(boolvar0, n) + bits).last ∨ bits0.last) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits0), bits0 = [], n = 0

Rule argument

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

Additional information

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