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Proof step 59 from proof fsync-inode-others-unchanged (previous step)

icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), err = ESUCCESS, err0 = ESUCCESS, files = files0, icache1 = icache0, inode = mkinode(m0, md, boolvar, m1, m2, m3), icache-cons(icache0, dirs, files0), pre-write-inode(inode, dirs, files), m ∈ icache0 ⊦ [icache_set_status#(m, false; err, icache1)] ( m0 = m ∧ (∀ ino0. ino0 ≠ m ∧ ino0 ∈ files0 → ino0 ∈ files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ] ∧ ( files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ] ⊕ icache1 )[ino0 ] = (files0 ⊕ icache0)[ino0])), inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 60:
icache0[m] = mkientry(true, mkinode(m0, md, false, files0[m0].nlink, 0, m3)), err = ESUCCESS, icache1 = icache0, icache-cons(icache0, dirs, files0), m0 ∈ files0, m ∈ icache0 ⊦ [icache_set_status#(m, false; err, icache1)] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0[m, (files0[m].meta:= md).size:= m3] ⊕ icache1)[ino] = (files0 ⊕ icache0)[ino]))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)