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Proof step 13 from proof inv-close (previous step)

err = ESUCCESS, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ ⟪afs_iget#(of[fd].ino, dirs, files, asynced; p_inode, err); if err = ESUCCESS then {of := of -- fd; vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ dom of < ino0 ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
of[fd] = mkfile(m, mode, m0), err = ESUCCESS, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ ⟪afs_iget#(m, dirs, files, asynced; p_inode, err); if err = ESUCCESS then {of := of -- fd; vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ dom of < ino0 ∧ afs-cons(dirs, files))

Rule argument

spec: file name: elim seq: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0) subst: [file, m, mode, m0] → [of[fd], m, mode, m0]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd], m, mode, m0