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Proof step 7 from proof path-fid (previous step)

dirs[ino0] = mkdir(m, md, m0, m1, entries), ((abs(tree, ino0) * D))(dirs), ispath(p0, entries[str], ino1, dirs, files), str ∈ entries, ino0 ∈ dirs, ino1 ∈ files, p0 ∈ tree[str '], str ' ∈ tree, ∀ tree, ino0, D, dirs, ino1, files. ((abs(tree, ino0) * D))(dirs) ∧ ispath(p0, ino0, ino1, dirs, files) ∧ p0 ∈ tree ∧ ino1 ∈ files → tree[p0] = fnode(⌜ino1⌝ ) ∨ ino1 ∈ dirs ⊦ tree[str ' + p0] = fnode(⌜ino1⌝ ), ino1 ∈ dirs

User applied rule constructor cut

And obtained the following new goals

Proof step 8:
dirs[ino0] = mkdir(m, md, m0, m1, entries), tree = dnode(md0, sdt), ((abs(tree, ino0) * D))(dirs), ispath(p0, entries[str], ino1, dirs, files), str ' ∈ tree, p0 ∈ tree[str '], ino1 ∈ files, ino0 ∈ dirs, str ∈ entries, ∀ tree, ino0, D, dirs, ino1, files. ((abs(tree, ino0) * D))(dirs) ∧ ispath(p0, ino0, ino1, dirs, files) ∧ p0 ∈ tree ∧ ino1 ∈ files → tree[p0] = fnode(⌜ino1⌝ ) ∨ ino1 ∈ dirs ⊦ tree[str ' + p0] = fnode(⌜ino1⌝ ), ino1 ∈ dirs

Rule argument

var: tree

Additional information

Used simplifier rules: directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;% ⊦ str ' ∈ fnode(fid) ↔ false; (s)