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Proof step 59 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files1[m] = mkfile(m0, md1, # links(m, dirs), content0), err = ESUCCESS, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m0, md1, # links(m, dirs), content0[n0, buf])]), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files1), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0 ⊦ ⟪afs_check_commit#(dirs, files1[m, mkfile(m0, md1, # links(m, dirs), content0[n0, buf])]; err; asynced1); n := n0; if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n := n + 1⟫ ( icache-cons(icache, dirs, files1[m, files1[m].content:= files1[m].content[n0, buf]]) ∧ dcache-cons(dcache, dirs, files1[m, files1[m].content:= files1[m].content[n0, buf]]) ∧ pcache-cons(pcache, dirs, files1[m, files1[m].content:= files1[m].content[n0, buf]]) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = files1[m].nlink ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 60:
# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m0, md1, # links(m, dirs), content0), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), files1[m] = mkfile(m3, md, m4, content1), err = ESUCCESS, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m0, md1, # links(m, dirs), content0[n0, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files1), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache ⊦ ⟪afs_check_commit#(dirs, files1[m, mkfile(m0, md1, # links(m, dirs), content0[n0, buf])]; err; asynced1); n := n0; if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n := n + 1⟫ ( icache-cons(icache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ dcache-cons(dcache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ pcache-cons(pcache, dirs, files1[m, files1[m].content:= content1[n0, buf]]) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = m4 ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

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] → [files1[m], m3, md, m4, content1]

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: files1[m], m3, md, m4, content1