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Proof step 11 from proof and-notempty (previous step)

bitsand(bits, bits0) = [] ⊦ bits = [], bits0 = [], bits0 = true ', bits0 = false ', bits ≠ bits.first ' ∧ bits0 ≠ bits0.first '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsand(bits, bits0) = bits0
Proof step 13:
¬(bits0 ≠ [] ∧ bits = true '), bitsand(bits, bits0) = [] ⊦ bits = [], bits0 = [], bits0 = true ', bits0 = false ', bits ≠ bits.first ' ∧ bits0 ≠ bits0.first '

Rule argument

name: and-rec-03 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used terms: bits0, bits