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Proof step 12 from proof inv-read (previous step)

err = ESUCCESS, dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n ≤ # buf, of[fd].mode ≠ MODE_R → fd ∈ of ⊦ ⟪afs_iget#(of[fd].ino, dirs, files, asynced; inode, err); if err = ESUCCESS then if inode.directory then err := EISDIR else let ino1 = of[fd].pos, ino0 = of[fd].pos + n, ino = 0 in if ino1 ≤ inode.size then {let isdir = false in vfs_read_loop#(ino1, ino0, inode, isdir, dirs, files, asynced; buf, ino, err); if ino ≠ 0 then err := ESUCCESS; of[fd].pos := of[fd].pos + ino; n := ino} else n := 0⟫ (of-cons(of, dirs, files) ∧ dom of < ino), of[fd].mode ≠ MODE_R ∧ of[fd].mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
of[fd] = mkfile(m, mode, m0), err = ESUCCESS, dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n ≤ # buf, mode ≠ MODE_R → fd ∈ of ⊦ ⟪afs_iget#(m, dirs, files, asynced; inode, err); if err = ESUCCESS then if inode.directory then err := EISDIR else let ino1 = m0, ino0 = m0 + n, ino = 0 in if ino1 ≤ inode.size then {let isdir = false in vfs_read_loop#(ino1, ino0, inode, isdir, dirs, files, asynced; buf, ino, err); if ino ≠ 0 then err := ESUCCESS; of[fd].pos := of[fd].pos + ino; n := ino} else n := 0⟫ (of-cons(of, dirs, files) ∧ dom of < ino), mode ≠ MODE_R ∧ mode ≠ MODE_RW

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