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Proof step 361 from proof inv-truncate-buff-none-cached (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 362:
# buf0 = 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(boolvar0, buf), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), 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))]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, datakey(m, m3) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # buf = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ (¬ boolvar0 → 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] → [(m = m0 ⊃ mkfile (m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[m] ), m4, md, m6, content]

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: (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[m] ), m4, md, m6, content