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Proof step 7 from proof add-ones-grlen-02 (previous step)

# bits0 ≤ # bits, ∀ bits, bits1. # bits1 < # bits0 → # bits1 ≤ # bits → bits1 = [] ∨ bitsand(bits, bits1) = bits1 ∨ false ∈ bits ∨ bits1.first ⊦ bitsand(bits, bits0) = bits0, bits0 = [], bits = [], bits0.first, false ∈ bits, # bits0 ≠ 1 ∧ # bits ≠ 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsand(bits, bits0) = bits
Proof step 9:
¬(bits ≠ [] ∧ bits0 = true '), # bits0 ≤ # bits, ∀ bits, bits1. # bits1 < # bits0 → # bits1 ≤ # bits → bits1 = [] ∨ bitsand(bits, bits1) = bits1 ∨ false ∈ bits ∨ bits1.first ⊦ bitsand(bits, bits0) = bits0, bits0 = [], bits = [], bits0.first, false ∈ bits, # bits0 ≠ 1 ∧ # bits ≠ 1

Rule argument

name: and-rec-01 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used simplifier rules: ⊦ boolvar ' ≠ [];% ⊦ # boolvar ' = 0 +1;% ⊦ boolvar '.first ↔ boolvar; Used terms: bits0, bits