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Proof step 137 from proof write-loop-term (previous step)

VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, files = files0 [m, mkfile(m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, zeropage, (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = n6 + min(n5, n7), n1 = n5 + n0 + n6, min(n5, n7) ≠ 0, afs-cons(dirs, files0), m ∈ files0, n6 ≤ # buf1, n5 + n6 ≤ # buf1, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7) ≤ VFS_PAGE_SIZE, n6 + min(n5, n7) ≤ # buf1, ¬ (n0 + n6) / VFS_PAGE_SIZE ∈ content, ∀ 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, buf1, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink)

User applied rule apply induction

And obtained the following new goals

Proof step 138:
VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, files = files0 [m, mkfile(m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, zeropage, (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = n6 + min(n5, n7), n1 = n5 + n0 + n6, afs-cons(dirs, files0), m ∈ files0, n6 + min(n5, n7) ≤ # buf1, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7) ≤ VFS_PAGE_SIZE, n5 + n6 ≤ # buf1, n6 ≤ # buf1, ∀ 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, buf1, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink), min(n5, n7) = 0, (n0 + n6) / VFS_PAGE_SIZE ∈ content, files[m] = mkfile(m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, zeropage, (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ∧ inode = mkinode(m, md, false, # links(m, dirs), 0, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n ≤ # buf1 ∧ n0 + n ≤ n1 ∧ n1 ≤ # buf1 + n0
Proof step 151:
⟪buf := buf1, n4 := n, n3 := n0, n2 := n1; 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), VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, files = files0 [m, mkfile(m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, zeropage, (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = n6 + min(n5, n7), n1 = n5 + n0 + n6, afs-cons(dirs, files0), m ∈ files0, n6 + min(n5, n7) ≤ # buf1, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7) ≤ VFS_PAGE_SIZE, n5 + n6 ≤ # buf1, n6 ≤ # buf1, ∀ 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, buf1, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink), min(n5, n7) = 0, (n0 + n6) / VFS_PAGE_SIZE ∈ content

Rule argument

subst: [n2, n3, n4, files, m, m1, md0, dirs, content, inode, md, m2, isdir, buf, err, asynced] → [n1, n0, n, files, m, m1, md0, dirs, content [(n0 + n6) / VFS_PAGE_SIZE, copy (buf1, n6, zeropage, (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7)) ], inode, md, m2, isdir, buf1, err, asynced]

Additional information

Used simplifier rules: ⊦ m + n - n + n1 = m - n1; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < min(n, m); (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s) Used terms: n1, n0, n, files, m, m1, md0, dirs, content [(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, zeropage, (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7)) ], inode, md, m2, isdir, buf1, err, asynced