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Proof step 25 from proof and-ass (previous step)

∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits1 = [], bits0 = [], bits = [], bitsand(bits, bitsand(bits0.butlast, bits1.butlast) + (bits0.last ∧ bits1.last)') = bitsand(bitsand(bits, bits0), bits1), bits0 = bits0.first ', bits1 = bits1.first '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 27:
¬(1 < # bits ∧ 1 < # bits0), ∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits1 = [], bits0 = [], bits = [], bitsand(bits, bitsand(bits0.butlast, bits1.butlast) + (bits0.last ∧ bits1.last)') = bitsand(bitsand(bits, bits0), bits1), bits0 = bits0.first ', bits1 = bits1.first '
Proof step 39:
1 < # bits ∧ 1 < # bits0, ∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits1 = [], bits0 = [], bits = [], bitsand(bits, bitsand(bits0.butlast, bits1.butlast) + (bits0.last ∧ bits1.last)') = bitsand(bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last), bits1), bits0 = bits0.first ', bits1 = bits1.first '

Rule argument

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

Additional information

Used terms: bits0, bits