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Proof step 348 from proof inv-truncate-buff-none-uncached (previous step)

# pcache0[datakey(m, m3)].page = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), 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), ¬ pcache0[datakey(m, m3)].dirty → m3 ∈ files0[m].content ∧ pcache0[datakey(m, m3)].page = files0[m].content[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])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 349:
# 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

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache0[datakey(m, m3)], boolvar0, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache0[datakey(m, m3)], boolvar0, buf0