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Proof step 289 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), pcache[key] = mkpentry(boolvar1, buf), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, key ∈ pcache ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ boolvar1 → key.part ∈ (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content ∧ buf = (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 290:
(key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]) = mkfile(m5, md1, m6, content), pcache[key] = mkpentry(boolvar1, buf), icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), key ∈ pcache, m ∈ files, m ∈ icache ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar1 → key.part ∈ content ∧ buf = content[key.part])

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] → [(key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2 ;files[key.ino] ), m5, md1, 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: (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]), m5, md1, m6, content