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Proof step 14 from proof and-size-one (previous step)

bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bitsand(bits.butlast, bits0 + bits1.butlast) + (bits1.last ∧ bits.last)' = bits0 + bitsand(bits, bits1), bits0 = [] ∧ bits1 = bits1.first '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 16:
¬(1 < # bits ∧ 1 < # bits1), bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bitsand(bits.butlast, bits0 + bits1.butlast) + (bits1.last ∧ bits.last)' = bits0 + bitsand(bits, bits1), bits0 = [] ∧ bits1 = bits1.first '
Proof step 20:
1 < # bits ∧ 1 < # bits1, bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bitsand(bits.butlast, bits0 + bits1.butlast) + (bits1.last ∧ bits.last)' = bits0 + (bitsand(bits.butlast, bits1.butlast) + (bits.last ∧ bits1.last)), bits0 = [] ∧ bits1 = bits1.first '

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [bits1, bits]

Additional information

Used terms: bits1, bits