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Proof step 1 from proof abs-files-evict (conclusion)

⊦ abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino = abs-files(fs, ri) -- ino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 3:
⊦ ∀ ino0. (ino0 ∈ abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino ↔ ino0 ∈ abs-files(fs, ri) -- ino) ∧ ( ino0 ∈ abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino → (abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino)[ino0] = (abs-files(fs, ri) -- ino)[ino0])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files0, files] → [abs-files(fs, ri) -- ino, abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino] flags: <all paths>

Additional information

Used terms: abs-files(fs, ri) -- ino, abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino