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Proof step 189 from proof inv-create (previous step)

files0[ino] = mkfile(m, md0, # links(ino, dirs0), content), icache0[ino] = mkientry(false, mkinode(ino, md0, false, # links(ino, dirs0), 0, m)), 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), ino ∈ icache0, m1 ∈ dirs0, ino ∈ files0, asynced1 → synced(files0, icache0, pcache), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files0 ∧ icache0[ino1].inode.nlink = files0[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files0) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files0[icache0[ino1].inode.ino].meta, false, files0[icache0[ino1].inode.ino].nlink, 0, files0[icache0[ino1].inode.ino].size) ) ), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = m1, ino0 = 0, mkinode(ino, md0, false, # links(ino, dirs0), 0, m) = mkinode(ino, (files0 ++ ino0)[ino].meta, false, (files0 ++ ino0)[ino].nlink, 0, (files0 ++ ino0)[ino].size), ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 190:
dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), icache0[ino] = mkientry(false, mkinode(ino, md0, false, # links(ino, dirs0), 0, m)), files0[ino] = mkfile(m, md0, # links(ino, dirs0), content), (files0 ++ ino0)[ino] = mkfile(m2, md3, m3, content0), 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), ino ∈ files0, m1 ∈ dirs0, ino ∈ icache0, asynced1 → synced(files0, icache0, pcache), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files0 ∧ icache0[ino1].inode.nlink = files0[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files0) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files0[icache0[ino1].inode.ino].meta, false, files0[icache0[ino1].inode.ino].nlink, 0, files0[icache0[ino1].inode.ino].size) ) ), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = m1, ino0 = 0, mkinode(ino, md0, false, # links(ino, dirs0), 0, m) = mkinode(ino, md3, false, m3, 0, m2), str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [(files0 ++ ino0)[ino], m2, md3, m3, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: (files0 ++ ino0)[ino], m2, md3, m3, content0