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Proof step 31 from proof dups-eqsize-ls (previous step)

∀ key0. key0 ∈ ks0 → key0.dentry?, ∀ key. key.dentry? → (key = dentrykey(m, str) ∨ key ∈ ks0 ↔ mklink(key.ino, key.name) = mklink(m, str) ∨ mklink(key.ino, key.name) ∈ ls0), ∀ ls1, ks. # ls1 < #(ls0 ++ mklink(m, str)) → (∀ key. key ∈ ks → key.dentry?) ∧ (∀ key. key.dentry? → (key ∈ ks ↔ mklink(key.ino, key.name) ∈ ls1)) → # ks = # ls1 ⊦ # ks0 = # ls0, dentrykey(m, str) ∈ ks0, mklink(m, str) ∈ ls0, (key ∈ ks0 → key.dentry?) ∧ (key0.dentry? → (key0 ∈ ks0 ↔ mklink(key0.ino, key0.name) ∈ ls0))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 4

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