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Proof step 131 from proof bitsor-bi-sgn (previous step)

bitsor(false ' + bits0, true ' + bits4) = false ' + bits2, bits2int(bitsor(sgn(false ' + bits0), true ' + bits4)) = bits2uint(bits2), true ∈ bits0, bitsor(sgn(false ' + bits0), true ' + bits4).first, boolvar ∨ boolvar0, ∀ bits, bits1. # bits1 < #((true + bits4) + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits2int(bitsor(sgn(false ' + bits0), true ' + bits4) + true ') = 1 + 2 * bits2uint(bits2), ¬ boolvar ∧ ¬ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 132:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsor(bits, bits0) = bitsor(bits0, bits)

Rule argument

name: bitsor-com rotate: F subst: [bits0, bits] → [true ' + bits4, false ' + bits0]

Additional information

Used simplifier rules: bitsor-first: ⊦ bits0 ≠ [] → bitsor(true ' + bits, bits0) ≠ false ' + bits1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: true ' + bits4, false ' + bits0