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Proof step 254 from proof eq-io-truncate (previous step)

files1[m] = mkfile(m0, md0, m1, content), m ∈ files1, ⌊err1⌋ , buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err = err1), ⟨let ino = m, content = files1[m].content, buf = ? in {pageno0 := m2 % VFS_PAGE_SIZE, pageno := min(n, m2); boolvar := m2 ≤ n ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?); files := files1; buf-opt := buf-opt0; if boolvar then {pageno1 := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno1]; buf := fill(buf, zero, pageno0, VFS_PAGE_SIZE - pageno0); content[pageno1] := buf; buf-opt := some(buf)}; files[ino].content := content upto pageno; let new_inode = mkinode(m, md, false, m1, 0, m2) in {new_inode.size := n; dirs0 := dirs1; afs_inode_sync#(new_inode; dirs1, files)}; inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS}; asynced := ?⟩ (buf-opt = buf-opt0 ∧ inode = mkinode(m, md, false, m1, 0, m2) ∧ (boolvar ↔ boolvar0) ∧ err = err1 ∧ dirs1 = dirs0 ∧ files = files1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 255:
files1[m] = mkfile(m0, md0, m1, content), files1[m] = mkfile(m3, md1, m4, content0), m ∈ files1, ⌊err1⌋ , buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err = err1), ⟨let ino = m, content = content0, buf = ? in {pageno0 := m2 % VFS_PAGE_SIZE, pageno := min(n, m2); boolvar := m2 ≤ n ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?); files := files1; buf-opt := buf-opt0; if boolvar then {pageno1 := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno1]; buf := fill(buf, zero, pageno0, VFS_PAGE_SIZE - pageno0); content[pageno1] := buf; buf-opt := some(buf)}; files[ino].content := content upto pageno; let new_inode = mkinode(m, md, false, m1, 0, m2) in {new_inode.size := n; dirs0 := dirs1; afs_inode_sync#(new_inode; dirs1, files)}; inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS}; asynced := ?⟩ (buf-opt = buf-opt0 ∧ inode = mkinode(m, md, false, m1, 0, m2) ∧ (boolvar ↔ boolvar0) ∧ err = err1 ∧ dirs1 = dirs0 ∧ files = files1)

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], m3, md1, m4, content0]

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], m3, md1, m4, content0