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Proof step 98 from proof fsync-dirs (previous step)

icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE, inode1.ino ∈ dirs0 ∧ inode1.nlink = dirs0[inode1.ino].nlink ∧ inode1.size = dirs0[inode1.ino].size ∧ inode1.nsubdirs = dirs0[inode1.ino].nsubdirs ∧ inode1.directory ∨ inode1.ino ∈ files ∧ inode1.nlink = files[inode1.ino].nlink ∧ inode1.nsubdirs = 0 ∧ ¬ inode1.directory ⊦ [fail#(; ; err); asynced := ?; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 99:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), inode1 = mkinode(m3, md, boolvar, m4, m5, m6), m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE, m3 ∈ dirs0 ∧ m4 = dirs0[m3].nlink ∧ m6 = dirs0[m3].size ∧ m5 = dirs0[m3].nsubdirs ∧ boolvar ∨ m3 ∈ files ∧ m4 = files[m3].nlink ∧ m5 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [inode1, m3, md, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode1, m3, md, boolvar, m4, m5, m6