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Proof step 43 from proof bitsxor-is-orand (previous step)

∀ bits, bits1. # bits1 < # true ' → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits = [], ~1 = bits2int(bits) + bits2int(bitsor(bitsinvert(bits), false '))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsor(bits, bits0) = bits

Rule argument

name: or-rec-02 rotate: F subst: [bits0, bits] → [false ', bitsinvert(bits)]

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ bits ≠ [] → bits2int(bitsinvert(bits)) = ~ bits2int(bits) - 1;% ⊦ ~ i - j = ~(i + j);% ⊦ i + ~ j = i - j;% ⊦ i - j + i = ~ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: false ', bitsinvert(bits)