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Proof step 137 from proof eq-io-truncate (previous step)

boolvar ↔ m2 ≤ n0 ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt.some?), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files2[m] = mkfile(m3, md1, m4, content), boolvar, content0 = content, dirs0 = dirs1, files = files2[ino, files2[ino].content:= (content0[pageno1, fill(files2[ino].content[pageno1], zero, pageno0, VFS_PAGE_SIZE - pageno0)] upto pageno)], ino = m, new_inode = mkinode(m, md, false, m4, 0, m2), pageno = min(n0, m2), pageno0 = m2 % VFS_PAGE_SIZE, pageno1 = m2 / VFS_PAGE_SIZE, m2 / VFS_PAGE_SIZE ∈ content, m ∈ files2, pageno1 ∈ files2[ino].content, m2 ≤ n0, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # files2[ino].content[pageno1], VFS_PAGE_SIZE ≥ pageno0, m2 ≤ n0 → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0 ⊦ ⟨afs_inode_sync#(new_inode.size:= n0; 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 := ?⟩ ( some(fill(files2[ino].content[pageno1], zero, pageno0, VFS_PAGE_SIZE - pageno0)) = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size);mkinode(m, md, false, m4, 0, n0)) ∧ boolvar ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files = files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), ⟨fail#(; ; err); asynced := ?⟩ ( buf-opt = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ mkinode(m, md, false, m4, 0, m2) = mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ∧ boolvar0 ∧ err = ESUCCESS ∧ files2 = files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, buf-opt.some?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 138:
VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files2[m] = mkfile(m3, md1, m4, content), dirs0 = dirs1, files = files2 [m, mkfile (m3, md1, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], m2 % VFS_PAGE_SIZE ≠ 0, m ∈ files2, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ n0, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], ¬ buf-opt.some? ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, m4, 0, n0); 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 := ?⟩ ( fill(files2[m].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) = fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size);mkinode(m, md, false, m4, 0, n0)) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files = files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), ⟨fail#(; ; err); asynced := ?⟩ ( buf-opt = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ mkinode(m, md, false, m4, 0, m2) = mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ∧ boolvar0 ∧ err = ESUCCESS ∧ files2 = files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)])

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ some(buf) = some(buf0) ↔ buf = buf0; (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2).size:= m6 = mkinode(m, md, boolvar, m0, m1, m6); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)