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Proof step 481 from proof inv-write_inode (previous step)

icache[m0] = mkientry(boolvar, mkinode(m0, md0, boolvar0, files[m0].nlink, m3, m4)), icache[ino] = mkientry(boolvar2, mkinode(m5, md1, boolvar1, m6, m7, m8)), afs-cons(dirs, files), synced(dirs, icache, pcache), m0 ∈ files, m0 ∈ icache, ino ∈ icache, (boolvar ⊃ m3 = 0 ∧ ¬ boolvar0 ;mkinode(m0, md0, boolvar0, files[m0].nlink, m3, m4) = mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ino = m0, m5 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m6 = files[ino].nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md1, boolvar1, m6, m7, m8) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 482:
icache[ino] = mkientry(boolvar2, mkinode(m5, md1, boolvar1, m6, m7, m8)), icache[m0] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), files[m0] = mkfile(m, md, m1, content), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m0 ∈ icache, m0 ∈ files, (boolvar ⊃ m3 = 0 ∧ ¬ boolvar0;mkinode(m0, md0, boolvar0, m1, m3, m4) = mkinode(m0, md, false, m1, 0, m)), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ino = m0, m5 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m6 = files[ino].nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md1, boolvar1, m6, m7, m8) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

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] → [files[m0], m, md, m1, 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: files[m0], m, md, m1, content