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Proof step 18 from proof fsync-inode-inv (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), asynced0, err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), icache[m].dirty, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache ⊦ ⟪icache_get#(m, icache; asynced0, inode, err); if err = ESUCCESS ∧ asynced0 then afs_write_inode#(inode; err, dirs, files; asynced1); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(boolvar, inode0), asynced0, boolvar, err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files ⊦ ⟪icache_get#(m, icache; asynced0, inode, err); if err = ESUCCESS ∧ asynced0 then afs_write_inode#(inode; err, dirs, files; asynced1); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[m], boolvar, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode0