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Proof step 7 from proof bitsand-app-ones (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
bits0 ≠ [], ∀ bits0, bits, bits2. # bits2 < # bits1 → true → bitsand(bits + true ' + bits0, false ' + bits2) = bitsand(true ' + bits0, false ' + bits2) ∨ false ∈ bits ⊦ bitsand(bits + true ' + bits0, false ' + bits1) = bitsand(true ' + bits0, false ' + bits1), false ∈ bits, bits0 ≠ [] ∧ bits1 ≠ []
Proof step 14:
∀ bits0, bits, bits2. # bits2 < # bits1 → true → bitsand(bits + true ' + bits0, false ' + bits2) = bitsand(true ' + bits0, false ' + bits2) ∨ false ∈ bits ⊦ bits0 ≠ [], bitsand(bits + true ' + bits0, false ' + bits1) = bitsand(true ' + bits0, false ' + bits1), false ∈ bits, bits0 ≠ [] ∧ bits1 ≠ []

Rule argument

fma: bits0 ≠ []

Additional information

Used formulas: bits0 ≠ []