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Proof step 11 from proof bitsor-first-02 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 12:
bits0 ≠ [], bitsor(false ' + bits0, false ' + bits2) = true ' + bits1, ∀ bits1, bits2, bits. # bits < # bits0 → bitsor(false ' + bits, false ' + bits2) = true ' + bits1 → false ⊦ bits0 ≠ [] ∧ bits2 ≠ []
Proof step 15:
bitsor(false ' + bits0, false ' + bits2) = true ' + bits1, ∀ bits1, bits2, bits. # bits < # bits0 → bitsor(false ' + bits, false ' + bits2) = true ' + bits1 → false ⊦ bits0 ≠ [], bits0 ≠ [] ∧ bits2 ≠ []

Rule argument

fma: bits0 ≠ []

Additional information

Used formulas: bits0 ≠ []