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Proof step 27 from proof new-inode-exists (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
inodekey(ino0) ∈ ks0, ino ≤ ino0, ∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino, ∀ ks1. # ks1 < #(ks0 ++ key) → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks1 → ino0 < ino) ⊦ # ks0 = 0, ks0 = ∅, key.inode?, key ∈ ks0

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ks ≠ ∅ → # ks ≠ 0; (forward) from specification set-basic[node-index]%ne-01: ⊦ key ∈ ks → ks ≠ ∅; (forward) from specification set-basic[node-index]% ⊦ inodekey(m).inode?; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)