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Proof step 138 from proof eq-io-truncate (previous step)

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)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 139:
VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE = n2 + 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, n2)] upto m2)], m2 / VFS_PAGE_SIZE ∈ content, m ∈ files2, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], m2 ≤ n0, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ ⟨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, n2) = 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)]), m2 % VFS_PAGE_SIZE = 0, buf-opt.some?

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n