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Proof step 143 from proof afs-cons-rename-file-dentry (previous step)

# links(entries0[str], dirs0) = m11 + 1, (entries0[str0] = entries0[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m1, md3, # links(entries0[str0], dirs0), content)) = mkfile(m14, md8, m15, content2), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries0[str0]] = mkfile(m1, md3, # links(entries0[str0], dirs0), content), dirs0[entries0[str0]] = mkdir(m16, md9, m17, m18, entries2), dirs0[m] = mkdir(m6 + 1, md6, # links(m, dirs0), m8, entries0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries0[str] ∈ files0, m ∈ dirs0, str ∈ entries0, entries0[str0] ∈ files0, str0 ∈ entries0, mklink(m, str) ∈ links(entries0[str0], dirs0) -- mklink(m, str0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m15 = #((links(entries0[str0], dirs0) -- mklink(m, str0)) ++ mklink(m, str)), mkdentry(str, entries0[str]) = mkdentry(str0, entries0[str0]), entries0[str] ∈ dirs0, entries0[str0] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 144:
# links(entries0[str], dirs0) = m15 + 1, files0[entries0[str]] = mkfile(m5, md0, m15 + 1, content1), dirs0[entries0[str]] = mkdir(m16, md9, m17, m18, entries2), dirs0[m] = mkdir(m6 + 1, md6, # links(m, dirs0), m8, entries0), entries0[str0] = entries0[str], afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, m ∈ dirs0, entries0[str] ∈ files0, str0 ∈ entries0, str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m15 = #(links(entries0[str], dirs0) -- mklink(m, str0)), mklink(m, str) = mklink(m, str0), entries0[str] ∈ dirs0

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkdentry(str, m) = mkdentry(str0, m0) ↔ str = str0 ∧ m = m0; (ws)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mklink(m, str).name = str; (s)% ⊦ mklink(m, str).pino = m; (s)%⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]; (s)% ⊦ alink ∈ ls -- alink0 ↔ alink ≠ alink0 ∧ alink ∈ ls; (s)% ⊦ alink ∈ ls → ls ++ alink = ls; (s)