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Proof step 349 from proof inv-truncate-buff-none-uncached (previous step)

# buf0 = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)] = mkpentry(boolvar, buf), pcache0[datakey(m, m3)] = mkpentry(boolvar0, buf0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m ∈ files0, datakey(m, m3) ∈ pcache0, m0 ∈ files0, ¬ boolvar0 → m3 ∈ files0[m].content ∧ buf0 = files0[m].content[m3], asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]), ∀ key. key ∈ pcache0 → key.data?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, # buf = VFS_PAGE_SIZE ∧ (¬ boolvar → m3 ∈ content ∧ buf = content[m3]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 350:
# buf0 = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), pcache0[datakey(m, m3)] = mkpentry(boolvar0, buf0), truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), files0[m] = mkfile(m7, md2, m8, content1), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache0), m0 ∈ files0, datakey(m, m3) ∈ pcache0, m ∈ files0, asynced2 → synced(files0, icache, pcache0), ¬ boolvar0 → m3 ∈ content1 ∧ buf0 = content1[m3], ∀ key. key ∈ pcache0 → key.data?, ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]), m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, # buf = VFS_PAGE_SIZE ∧ (¬ boolvar → m3 ∈ content ∧ buf = content[m3])

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] → [files0[m], m7, md2, m8, 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: files0[m], m7, md2, m8, content1