| # bits1 < # bits, ∀ bits, bits0. # bits0 < # bits1 → # bits0 < # bits → # bitsand(bits, false ' + bits0) = 1 + # bits0 ∨ bits = [] ⊦ # bitsand(bits, false ' + bits1) = 1 + # bits1 ∨ bits = [] |
# bits1 < # bits, ∀ bits, bits0. # bits0 < # bits1 → # bits0 < # bits → # bitsand(bits, false ' + bits0) = 1 + # bits0 ∨ bits = [] ⊦ bits = [], # bitsand(bits, false ' + bits1) = 1 + # bits1