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Proof step 7 from proof bitsxor-is-orand (previous step)

∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits0), bitsand(bitsinvert(bits0), bits))), bits0 = [], bits = [], # bits ≠ 1 ∧ # bits0 ≠ 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsand(bits, bits0) = bits
Proof step 9:
¬(bitsinvert(bits) ≠ [] ∧ bits0 = true '), ∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits0), bitsand(bitsinvert(bits0), bits))), bits0 = [], bits = [], # bits ≠ 1 ∧ # bits0 ≠ 1
Proof step 39:
bitsinvert(bits) ≠ [] ∧ bits0 = true ', ∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsinvert(bits), bitsand(bitsinvert(bits0), bits))), bits0 = [], bits = [], # bits ≠ 1 ∧ # bits0 ≠ 1

Rule argument

name: and-rec-01 rotate: F subst: [bits0, bits] → [bits0, bitsinvert(bits)]

Additional information

Used terms: bits0, bitsinvert(bits)