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Proof step 43 from proof fsync-inode-inv (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(true, mkinode(m1, md, boolvar, m2, m3, m4)), err = ESUCCESS, 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, m1 ∈ dirs ∧ m2 = dirs[m1].nlink ∧ m4 = dirs[m1].size ∧ m3 = dirs[m1].nsubdirs ∧ boolvar ∨ m1 ∈ files ∧ m2 = files[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar ⊦ [afs_write_inode#(mkinode(m1, md, boolvar, m2, m3, m4); err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪inode := mkinode(m1, md, boolvar, m2, m3, m4); 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) ∧ 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 44:
icache[m] = mkientry(true, mkinode(m1, md, boolvar, m2, m3, m4)), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, m6, content0), err = ESUCCESS, 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, m1 ∈ dirs ∧ m2 = dirs[m1].nlink ∧ m4 = dirs[m1].size ∧ m3 = dirs[m1].nsubdirs ∧ boolvar ∨ m1 ∈ files ∧ m2 = m6 ∧ m3 = 0 ∧ ¬ boolvar ⊦ [afs_write_inode#(mkinode(m1, md, boolvar, m2, m3, m4); err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪inode := mkinode(m1, md, boolvar, m2, m3, m4); 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) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory))

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] → [files[m1], m5, md1, m6, 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: files[m1], m5, md1, m6, content0