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Proof step 59 from proof refine-read (previous step)

of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), buf = buf0, err = ESUCCESS, ino3 = 0, root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), fd ∈ of, m0 ≤ m1, n0 ≤ # buf0, psynced → asynced ⊦ [vfs_read_loop#(m0, m0 + n0, mkinode(m, md, false, m2, 0, m1), false, dirs, files, asynced; buf, ino3, err); if ino3 ≠ 0 then err := ESUCCESS; of0 := of[fd, of[fd].pos:= (of[fd].pos + ino3)]; n := ino3] ( of-cons(of0, dirs, files) ∧ dom of0 < ino2 → ⟨ofh := abs-of(of); posix_read#(fd, user, root, abs-files(files); buf0, n0, err0, ofh)⟩ (ofh = abs-of(of0) ∧ (psynced → asynced) ∧ buf = buf0 ∧ n = n0 ∧ err = err0)), mode ≠ MODE_R ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 60:
files[m] = mkfile(m1, md, m2, content), of[fd] = mkfile(m, mode, m0), of[fd] = mkfile(m3, mode0, m4), buf = buf0, err = ESUCCESS, ino3 = 0, root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), fd ∈ of, n0 ≤ # buf0, m0 ≤ m1, psynced → asynced ⊦ [vfs_read_loop#(m0, m0 + n0, mkinode(m, md, false, m2, 0, m1), false, dirs, files, asynced; buf, ino3, err); if ino3 ≠ 0 then err := ESUCCESS; of0 := of[fd, of[fd].pos:= (m4 + ino3)]; n := ino3] ( of-cons(of0, dirs, files) ∧ dom of0 < ino2 → ⟨ofh := abs-of(of); posix_read#(fd, user, root, abs-files(files); buf0, n0, err0, ofh)⟩ (ofh = abs-of(of0) ∧ (psynced → asynced) ∧ buf = buf0 ∧ n = n0 ∧ err = err0)), 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], m3, mode0, m4]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd], m3, mode0, m4