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Proof step 23 from proof new-inode-exists (previous step)

∀ 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

User applied rule exists right

And obtained the following new goals

Proof step 24:
∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino, ∀ ks1. # ks1 < #(ks0 ++ inodekey(m)) → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks1 → ino0 < ino) ⊦ inodekey(m) ∈ ks0, ∀ ino0. ino0 = m ∨ inodekey(ino0) ∈ ks0 → ino0 < ino + m + 1

Rule argument

pos: right 2 terms: ino + m + 1 abort: F discard: T computed: F

Additional information

Used terms: ino + m + 1