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Proof step 15 from proof bitsand-app-ones (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ ¬ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits0
Proof step 17:
¬(¬ false ∈ bits + true ' ∧ #(false ' + bits1) ≤ #(bits + true ') ∧ ¬ (false ' + bits1).first ∧ false ' + bits1 ≠ []), ∀ bits0, bits, bits2. # bits2 < # bits1 → true → bitsand(bits + true ' + bits0, false ' + bits2) = bitsand(true ' + bits0, false ' + bits2) ∨ false ∈ bits ⊦ bitsand(bits + true ', false ' + bits1) = false ' + bits1, false ∈ bits

Rule argument

name: add-ones-grlen-02 rotate: F subst: [bits0, bits] → [false ' + bits1, bits + true ']

Additional information

Used terms: false ' + bits1, bits + true '