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Proof step 121 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), key ∈ pcache, m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ (key.ino = ino0 ∨ key.ino ∈ files0) ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]).content ∧ pcache[key].page = (key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 122:
dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, key ∈ pcache, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ (key.ino = ino0 ∨ key.ino ∈ files0) ∧ ( ¬ boolvar → key.part ∈ (key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]).content ∧ buf = (key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]).content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[key], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key], boolvar, buf