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Proof step 14 from proof inv-truncate-buff-none-uncached (previous step)

# links(m, dirs) = files[m].nlink, files[m] = mkfile(m0, md0, files[m].nlink, content), ¬ asynced0, ¬ asynced1, 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, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced → synced(files, icache, pcache) ⊦ ⟪pcache_check_page#(m, m2 / VFS_PAGE_SIZE, pcache; asynced1, asynced0, err); pageno := m2 / VFS_PAGE_SIZE; if err = ESUCCESS ∧ asynced1 then pcache_get#(m, pageno, pcache; asynced1, buf, err); buf-opt := none; if err = ESUCCESS ∧ asynced1 then buf-opt := some(buf); size := m2; inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if err = ESUCCESS then afs_truncate#(n, pageno; buf-opt, inode, asynced4, err, dirs, files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, size, n; err, pcache); if asynced4 then pcache_set#(inode.ino, pageno, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
# links(m, dirs) = m3, files[m] = mkfile(m0, md0, m3, content), files[m] = mkfile(m1, md1, m3, content0), ¬ asynced0, ¬ asynced1, 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, asynced → synced(files, icache, pcache) ⊦ ⟪pcache_check_page#(m, m2 / VFS_PAGE_SIZE, pcache; asynced1, asynced0, err); pageno := m2 / VFS_PAGE_SIZE; if err = ESUCCESS ∧ asynced1 then pcache_get#(m, pageno, pcache; asynced1, buf, err); buf-opt := none; if err = ESUCCESS ∧ asynced1 then buf-opt := some(buf); size := m2; inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if err = ESUCCESS then afs_truncate#(n, pageno; buf-opt, inode, asynced4, err, dirs, files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, size, n; err, pcache); if asynced4 then pcache_set#(inode.ino, pageno, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache

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[m], m1, md1, 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: files[m], m1, md1, m3, content0