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Proof step 3 from proof and-notone-01 (previous step)

bitsand(bits, false ' + bits0) = true ' + bits1, ∀ bits2, bits0, bits1. # bits2 < # bits → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 5:
¬(1 < # bits ∧ 1 < #(false ' + bits0)), bitsand(bits, false ' + bits0) = true ' + bits1, ∀ bits2, bits0, bits1. # bits2 < # bits → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits = []
Proof step 10:
1 < # bits ∧ 1 < #(false ' + bits0), bitsand(bits.butlast, (false ' + bits0).butlast) + (bits.last ∧ (false ' + bits0).last) = true ' + bits1, ∀ bits2, bits0, bits1. # bits2 < # bits → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits = []

Rule argument

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

Additional information

Used terms: false ' + bits0, bits