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Proof step 13 from proof and-notone-01 (previous step)

bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast) + (bits0.last ∧ bits3.last)' = true ' + bits1, ∀ bits2, bits0, bits1. # bits2 < #(boolvar + bits3) → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits3 = [], bits0 = [], (¬ bits3.last ∨ ¬ bits0.last) ∧ ¬ true ∈ bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast), ¬ (bits3.last ∧ bits0.last) ∈ bits1 ∧ (¬ bits3.last ∨ ¬ bits0.last), (¬ bits0.last ∨ ¬ bits3.last) ∧ ¬ (bits0.last ∧ bits3.last) ∈ bits1, ¬ true ∈ bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast) ∧ (¬ bits0.last ∨ ¬ bits3.last)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
bits ≠ [] ⊦ bits0 + boolvar ' = bits ↔ bits0 = bits.butlast ∧ (boolvar ↔ bits.last)
Proof step 15:
true ' + bits1 ≠ [], bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast) = (true ' + bits1).butlast ∧ (bits0.last ∧ bits3.last ↔ (true ' + bits1).last), ∀ bits2, bits0, bits1. # bits2 < #(boolvar + bits3) → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits3 = [], bits0 = [], (¬ bits3.last ∨ ¬ bits0.last) ∧ ¬ true ∈ bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast), ¬ (bits3.last ∧ bits0.last) ∈ bits1 ∧ (¬ bits3.last ∨ ¬ bits0.last), (¬ bits0.last ∨ ¬ bits3.last) ∧ ¬ (bits0.last ∧ bits3.last) ∈ bits1, ¬ true ∈ bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast) ∧ (¬ bits0.last ∨ ¬ bits3.last)

Rule argument

seq: bits ≠ [] ⊦ bits0 + boolvar ' = bits ↔ bits0 = bits.butlast ∧ (boolvar ↔ bits.last) subst: [bits, boolvar, bits0] → [true ' + bits1, bits0.last ∧ bits3.last, bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast)] rotate: F spec: list-last inst: bitlista name: splitlasteq

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: true ' + bits1, bits0.last ∧ bits3.last, bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast)