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Proof step 1 from proof size-rem (conclusion)

⊦ (as -- adr).size = as.size - (adr ∈ as ⊃ adr.size;0)

User applied rule case distinction

And obtained the following new goals

Proof step 2:
adr ∈ as ⊦ (as -- adr).size = as.size - adr.size

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ as → as -- adr = as; (s)% ⊦ m - 0 = m; (s)