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Proof step 11 from proof eq-io-lookup (previous step)

⟨if pre-lookup(p_ino, dent, dirs, files) then { if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT} or fail#(; ; err)} else abort⟩ (dent = old_dent ∧ err = err1), asynced ↔ asynced0, dirs1[pageno] = mkdir(m, md, m0, m1, entries), dirs = dirs1, files = files1, p_ino = pageno, pageno ∈ dirs1, links(pageno, dirs1) ≠ ∅ ∨ pageno = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (dent = old_dent ∧ err = err1), ⟨if dent.name ∈ entries then {dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ (dent = old_dent ∧ err = err1)

Heuristic symbolic execution applied rule if positive left

And obtained the following new goals

Proof step 12:
⟨ if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT} or fail#(; ; err)⟩ (dent = old_dent ∧ err = err1), asynced ↔ asynced0, dirs1[pageno] = mkdir(m, md, m0, m1, entries), dirs = dirs1, files = files1, p_ino = pageno, pageno ∈ dirs1, links(pageno, dirs1) ≠ ∅ ∨ pageno = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (dent = old_dent ∧ err = err1), ⟨if dent.name ∈ entries then {dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ (dent = old_dent ∧ err = err1)

Rule argument

pos: left 1

Additional information

Used simplifier rules: ⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)