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Proof step 39 from proof bitsor-mklist-in (previous step)

∀ bits, boolvar0, boolvar, n, bits1. # bits1 < #(bits3 + boolvar2 ') → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ n = 0, boolvar ∈ bitsor(mklist(boolvar0, n) + bits2, bits3) ∨ (boolvar ↔ boolvar1 ∨ boolvar2) ↔ boolvar ∈ bitsor(boolvar0 ' + bits2 + boolvar1 ', bits3 + boolvar2 '), bits3 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsor(bits, bits0) = bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last)
Proof step 41:
1 < #(boolvar0 ' + bits2 + boolvar1 ') ∧ 1 < #(bits3 + boolvar2 '), ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < #(bits3 + boolvar2 ') → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ n = 0, boolvar ∈ bitsor(mklist(boolvar0, n) + bits2, bits3) ∨ (boolvar ↔ boolvar1 ∨ boolvar2) ↔ boolvar ∈ bitsor((boolvar0 ' + bits2 + boolvar1 ').butlast, (bits3 + boolvar2 ').butlast) + ((boolvar0 ' + bits2 + boolvar1 ').last ∨ (bits3 + boolvar2 ').last), bits3 = []

Rule argument

name: or-rec rotate: F subst: [bits0, bits] → [bits3 + boolvar2 ', boolvar0 ' + bits2 + boolvar1 ']

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;%n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ m + 1 ≠ 0;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = []; Used terms: bits3 + boolvar2 ', boolvar0 ' + bits2 + boolvar1 '