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Proof step 20 from proof new-inode-exists (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ key.inode? ↔ (∃ m. key = inodekey(m))
Proof step 22:
∀ 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

Rule argument

spec: key name: ex-02 seq: ⊦ key.inode? ↔ (∃ m. key = inodekey(m)) subst: [key] → [key] flags: <all paths>

Additional information

Used terms: key