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Proof step 101 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), 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, ∅)]), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, ∀ ino. (ino ∈ dirs0 → synced(ino, icache0, pcache)) → ino ∈ dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])] → synced (ino, icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ], pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 102:
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), synced(dirs0, icache0, pcache), m1 ∈ dirs0, ino ∈ dirs0, asynced1 → synced(files0, icache0, pcache), ino ∈ icache0 → ¬ icache0[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, ( ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] → ¬ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty)

Rule argument

Additional information

Used simplifier rules: ⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)