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Proof step 8 from proof add-ones-grlen (previous step)

# bits = n + 1 + # bits1, # bits1 < # bits, ∀ bits0, bits, n. # bits0 < # bits1 → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bitsand(bits, true ' + bits1) = (true ' + mklist(true, n)) + bits1, bits = [], false ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 10:
¬(1 < # bits ∧ 1 < #(true ' + bits1)), # bits = n + 1 + # bits1, # bits1 < # bits, ∀ bits0, bits, n. # bits0 < # bits1 → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bitsand(bits, true ' + bits1) = (true ' + mklist(true, n)) + bits1, bits = [], false ∈ bits
Proof step 15:
1 < # bits ∧ 1 < #(true ' + bits1), # bits = n + 1 + # bits1, # bits1 < # bits, ∀ bits0, bits, n. # bits0 < # bits1 → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bitsand(bits.butlast, (true ' + bits1).butlast) + (bits.last ∧ (true ' + bits1).last) = (true ' + mklist(true, n)) + bits1, bits = [], false ∈ bits

Rule argument

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

Additional information

Used terms: true ' + bits1, bits