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Proof step 15 from proof write-loop-term (previous step)

files[m] = mkfile(m1, md0, # links(m, dirs), content), inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, afs-cons(dirs, files), m ∈ files, n ≤ # buf, n0 + n ≤ n1, n1 ≤ # buf + n0, ∀ n2, n3, n4, files, m, m1, md0, dirs, content, inode, md, m2, isdir, buf, err, asynced. n2 - n3 + n4 < n1 - n0 + n → files[m] = mkfile(m1, md0, # links(m, dirs), content) ∧ inode = mkinode(m, md, false, # links(m, dirs), 0, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n3, inode, buf, n2, dirs; n4, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink) ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
files[m] = mkfile(m1, md0, # links(m, dirs), content), inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n1 = n5 + n0 + n, afs-cons(dirs, files), m ∈ files, n1 ≤ # buf + n0, n0 + n ≤ n1, n ≤ # buf, ∀ n2, n3, n4, files, m, m1, md0, dirs, content, inode, md, m2, isdir, buf, err, asynced. n2 - n3 + n4 < n5 → files[m] = mkfile(m1, md0, # links(m, dirs), content) ∧ inode = mkinode(m, md, false, # links(m, dirs), 0, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n3, inode, buf, n2, dirs; n4, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink) ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n0 + n, n1, n5]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0 + n, n1, n5