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Proof step 12 from proof bitsor-bi-sgn (previous step)

# bits = 1, ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits = [], bits0 = [], bits2int(bitsor(sgn(bits), bits0)) = bits2int(bitsor(bits, bits0)), bits0 = true ', bits0 = false ', # bits0 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsor(bits, bits0) = true '
Proof step 14:
bits0 ≠ [] ∧ bits = true ', # bits = 1, ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits = [], bits0 = [], bits2int(bitsor(sgn(bits), bits0)) = bits2int(true '), bits0 = true ', bits0 = false ', # bits0 = 1

Rule argument

name: or-rec-03 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used simplifier rules: ⊦ # bits = 1 ∧ bits ≠ true ' → bits = false '; (forward)% ⊦ # boolvar ' = 0 +1;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ sgn(boolvar ') = boolvar ';% ⊦ boolvar ' ≠ []; Used terms: bits0, bits