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Proof step 226 from proof refine-read (previous step)

files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), root.dir?, m1 < m0, 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), m ∈ files, fd ∈ of, n0 ≤ # buf0, psynced → asynced ⊦ (¬ n ≤ n0 ∨ ¬ of[fd].pos + n ≤ files[of[fd].ino].size) ∧ ⟨n0 := 0⟩ ((psynced → asynced) ∧ 0 = n0), ∃ n1. n1 ≤ n0 ∧ of[fd].pos + n1 ≤ files[of[fd].ino].size ∧ ⟨n0 := n1; buf := copy(abs-files(files)[abs-of(of)[fd].fid].content, abs-of(of)[fd].pos, buf0, 0, n0); ofh := abs-of(of)[fd, mkfh(abs-of(of)[fd].fid, abs-of(of)[fd].mode, abs-of(of)[fd].pos + n0)]⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ buf0 = buf ∧ 0 = n0), mode ≠ MODE_R ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 227:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content), abs-of(of)[fd] = mkfh(fid, mode0, m2), root.dir?, dom of < ino2, m1 < m0, 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, m ∈ files, n0 ≤ # buf0, psynced → asynced ⊦ (¬ n ≤ n0 ∨ ¬ of[fd].pos + n ≤ files[of[fd].ino].size) ∧ ⟨n0 := 0⟩ ((psynced → asynced) ∧ 0 = n0), ∃ n1. n1 ≤ n0 ∧ of[fd].pos + n1 ≤ files[of[fd].ino].size ∧ ⟨n0 := n1; buf := copy(abs-files(files)[fid].content, m2, buf0, 0, n0); ofh := abs-of(of)[fd, mkfh(fid, mode0, m2 + n0)]⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ buf0 = buf ∧ 0 = n0), mode ≠ MODE_R ∧ mode ≠ MODE_RW

Rule argument

spec: file-handle name: elim seq: ⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m) subst: [fh, fid, mode, m] → [abs-of(of)[fd], fid, mode0, m3]

Additional information

Used simplifier rules: ⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m); (elim) Used terms: abs-of(of)[fd], fid, mode0, m3