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Proof step 15 from proof write-inode-inv (previous step)

files1[ino].meta = md, files = files1, inode = mkinode(ino, files1[ino].meta, false, m, n0, m0 + n), pre-write-inode(inode, dirs, files), write-inv(n0, n1, mkinode(ino, files1[ino].meta, false, m, n0, m0), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, n0, files0[ino, files0[ino].size:= (m0 + n)][ino].size), buf, n, dirs, files0[ino, files0[ino].size:= (m0 + n)], 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0
Proof step 17:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1
Proof step 18:
write-inv(0, n1, mkinode(ino, files1[ino].meta, false, files1[ino].nlink, 0, m0), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ write-inv (0, n1, mkinode(ino, files1[ino].meta, false, files1[ino].nlink, 0, m0 + n), buf, n, dirs, files0[ino, files0[ino].size:= (m0 + n)], files1[ino, (files1[ino].meta:= files1[ino].meta).size:= (m0 + n)])

Rule argument

Additional information

Used simplifier rules: write-inv-in1: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0;%write-inv-in0: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1;% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ (af.size:= m).size = m; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (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)% ⊦ 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).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)