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Proof step 3 from proof abs-files-put-nlink (previous step)

files[ino] = mkfile(m, md, n0, content), ino ∈ files ⊦ abs-files(files[ino, mkfile(m, md, n1, content)]) = abs-files(files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ fs = fs0 ↔ (∀ fid. (fid ∈ fs ↔ fid ∈ fs0) ∧ (fid ∈ fs → fs[fid] = fs0[fid]))
Proof step 5:
files[ino] = mkfile(m, md, n0, content), ino ∈ files ⊦ ∀ fid. (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) ↔ fid ∈ abs-files(files)) ∧ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) → abs-files(files[ino, mkfile(m, md, n1, content)])[fid] = abs-files(files)[fid])

Rule argument

spec: store, inst: file-data-store name: k-Extension seq: ⊦ fs = fs0 ↔ (∀ fid. (fid ∈ fs ↔ fid ∈ fs0) ∧ (fid ∈ fs → fs[fid] = fs0[fid])) subst: [fs0, fs] → [abs-files(files), abs-files(files[ino, mkfile(m, md, n1, content)])] flags: <all paths>

Additional information

Used terms: abs-files(files), abs-files(files[ino, mkfile(m, md, n1, content)])