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Proof step 468 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))], m ∈ files, m ∈ icache ⊦ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty ⊃ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino ∈ files ∧ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.nlink = files[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].nlink ∧ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode = (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino, dirs[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].meta, true, dirs[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].nlink, dirs[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].nsubdirs, dirs[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].size) ;mkinode (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino, files[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].meta, false, files[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].nlink, 0, files[icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 469:
icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode = mkinode(m5, md1, boolvar1, m6, m7, m8), icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, ino ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] ⊦ m5 = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty ⊃ m5 ∈ files ∧ m6 = files[m5].nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode = (m5 ∈ dirs ⊃ mkinode(m5, dirs[m5].meta, true, dirs[m5].nlink, dirs[m5].nsubdirs, dirs[m5].size) ;mkinode(m5, files[m5].meta, false, files[m5].nlink, 0, files[m5].size) ) )

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache [m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2)) ] [ino ] .inode, m5, md1, boolvar1, m6, m7, m8]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino] .inode, m5, md1, boolvar1, m6, m7, m8