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Proof step 7 from proof and-size-one (previous step)

bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1), bits = [], (bits0 ≠ [] ∨ bits1 ≠ []) ∧ # bits0 + # bits1 ≠ 1 ∧ bits ≠ true '

User applied rule cut formula

And obtained the following new goals

Proof step 8:
bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits1 = [], bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1), bits = [], (bits0 ≠ [] ∨ bits1 ≠ []) ∧ # bits0 + # bits1 ≠ 1 ∧ bits ≠ true '

Rule argument

fma: bits1 = []

Additional information

Used simplifier rules: ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # [] = 0;% ⊦ m ≤ 0 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = []; Used formulas: bits1 = []