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Proof step 105 from proof eq-io-truncate (previous step)

⟨afs_inode_sync#(mkinode(m, md, false, m1, 0, n0); dirs1, files1)⟩ (dirs1 = dirs0 ∧ files1 = files0), files2[m] = mkfile(m0, md0, m1, content0), files = files2, files1 = files2 [m, mkfile (m0, md0, m1, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md, false, m1, 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, m ∈ files2, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ n0, VFS_PAGE_SIZE ≤ # content0[m2 / VFS_PAGE_SIZE], ¬ buf-opt.some? ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode, boolvar1, err, dirs1, files2, boolvar2)⟩ ( buf-opt = some(fill(files[m].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar1 ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files2 = files0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 106:
⟨afs_inode_sync#(mkinode(m, md, false, m1, 0, n0); dirs1, files1)⟩ (dirs1 = dirs0 ∧ files1 = files0), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files2[m] = mkfile(m0, md0, m1, content0), files = files2, files1 = files2[m, mkfile(m0, md0, m1, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)], inode = mkinode(m, md, false, m1, 0, m2), m2 / VFS_PAGE_SIZE ∈ content0, m ∈ files2, VFS_PAGE_SIZE ≤ # content0[m2 / VFS_PAGE_SIZE], m2 ≤ n0, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode, boolvar1, err, dirs1, files2, boolvar2)⟩ ( buf-opt = some(fill(files[m].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, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar1 ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files2 = files0), 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