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Proof step 360 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, 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, # truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)].page = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ ( ¬ truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)].dirty → m3 ∈ (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).content ∧ truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)].page = (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).content[m3])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 361:
# 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

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)], boolvar0, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)], boolvar0, buf