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Proof step 7 from proof and-ass (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits0 ≠ bits0.first ', bitsand(bits, bitsand(bits0, bits1)) = bitsand(bitsand(bits, bits0), bits1), bits1 = [], bits0 = [], bits = []
Proof step 13:
∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits1 ≠ bits1.first ', bitsand(bits, bitsand(bits0, bits1)) = bitsand(bitsand(bits, bits0), bits1), bits1 = [], bits0 = [], bits = []

Rule argument

pos: right 5

Proof step 7 from proof and-ass (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information