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Proof step 60 from proof write-prepost-partial (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, m3, content), buf-opt = none, err = ESUCCESS, files2 = files0, content.stream from m1 = σ⊥, ino0 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files1, fd ∈ of1, n1 ≤ # buf ⊦ ∀ ino0, err, files0, asynced0. err = ESUCCESS ∨ ⌊err⌋ → (ino0 = 0 → files0 = files2) → write-inv(of1[fd].pos, of1[fd].pos + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino0, dirs0, files2, files0) → [if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = m1 in {n := ino0, ino1 := of1[fd].pos + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files0; err; asynced0); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs0, files0; asynced0)}; ino2 := of1[fd].pos; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files0[m].content.stream to files0[m].size).buf = splice(buf, 0, (content0.stream to m1).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files0 ∧ files0[m].meta = md ∧ files0 -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files0 ~ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1
Proof step 62:
⊦ write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1
Proof step 63:
⊦ write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1
Proof step 64:
⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, m3, content), buf-opt = none, err = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), n1 ≠ 0, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, ino = 0 → files = files0, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ [if ino ≠ 0 then err0 := ESUCCESS; of := of1; n := n1; if err0 = ESUCCESS then let ino3 = m1 in {n := ino, ino1 := of1[fd].pos + ino; if ino ≠ 0 ∧ ino3 < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files; err0; asynced1); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs0, files; asynced1)}; ino2 := of1[fd].pos; if err0 ≠ ESUCCESS then n := (ino2 ≤ ino3 ⊃ ino3 - ino2;0), err0 := ESUCCESS; of[fd].pos := ino2 + n}] (err0 = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content0.stream to m1).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files ∧ files[m].meta = md ∧ files -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err0 = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err0⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: write-inv-in0: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1;%write-inv-ls: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1;%write-inv-ls: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1;% ⊦ mkfile(m, mode, m0).pos = m0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic