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Proof step 22 from proof new-inode-exists (previous step)

∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino, ∃ m. key = inodekey(m), ∀ ks1. # ks1 < #(ks0 ++ key) → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks1 → ino0 < ino) ⊦ key ∈ ks0, ∃ ino. ∀ ino0. inodekey(ino0) = key ∨ inodekey(ino0) ∈ ks0 → ino0 < ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino, ∀ ks1. # ks1 < #(ks0 ++ inodekey(m)) → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks1 → ino0 < ino) ⊦ inodekey(m) ∈ ks0, ∃ ino1. ∀ ino0. ino0 = m ∨ inodekey(ino0) ∈ ks0 → ino0 < ino1

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)