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Proof step 31 from proof write-prepost-partial (previous step)

of1[fd] = mkfile(m, mode, m0), buf-opt = none, err = ESUCCESS, files = files1, inode = mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size), n1 ≠ 0, afs-cons(dirs, files1), of-cons(of1, dirs, files1), fd ∈ of1, n1 ≤ # buf ⊦ [afs_truncate#(files1[m].size, files1[m].size / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced); ino2 := of1[fd].pos; ino0 := 0; if err = ESUCCESS then vfs_write_loop#(ino2, inode, of1[fd].pos + n1, buf, dirs; ino0, err, files, asynced); if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = inode.size in {n := ino0, ino1 := ino2 + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (files1[m].content.stream to files1[m].size).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files1 ∧ m ∈ files ∧ files[m].meta = files1[m].meta ∧ files -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, m2, content), buf-opt = none, err = ESUCCESS, files = files1, inode = mkinode(m, md, false, m2, 0, m1), afs-cons(dirs, files1), of-cons(of1, dirs, files1), fd ∈ of1, n1 ≤ # buf ⊦ [afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced); ino2 := of1[fd].pos; ino0 := 0; if err = ESUCCESS then vfs_write_loop#(ino2, inode, of1[fd].pos + n1, buf, dirs; ino0, err, files, asynced); if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = inode.size in {n := ino0, ino1 := ino2 + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content.stream to m1).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files1 ∧ m ∈ files ∧ files[m].meta = md ∧ files -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files1[m], m1, md, m2, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files1[m], m1, md, m2, content