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Proof step 96 from proof read-loop-term (previous step)

0 = min(n5, VFS_PAGE_SIZE - (n0 + n2) % VFS_PAGE_SIZE, n1), err = ESUCCESS, ino1 = n5 + n0 + n2, inode = mkinode(m, md, boolvar, m0, m1, n1 + n0 + n2), isdir, afs-cons(dirs, files), m ∈ files, n2 ≤ # buf2, n5 + n2 ≤ # buf2, ∀ n2, n3, n4, err, inode, m, md, boolvar, m0, m1, m2, isdir, dirs, files, buf, asynced. n2 - n3 + n4 < n5 → err = ESUCCESS ∧ inode = mkinode(m, md, boolvar, m0, m1, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ m2 ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err); while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err)⟫ true ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, ino1, inode, dirs, files, asynced; buf2, n2, isdir, err)⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 97:
0 = min(n5, n6, n1), VFS_PAGE_SIZE = n6 + (n0 + n2) % VFS_PAGE_SIZE, err = ESUCCESS, ino1 = n5 + n0 + n2, inode = mkinode(m, md, boolvar, m0, m1, n1 + n0 + n2), isdir, afs-cons(dirs, files), m ∈ files, n5 + n2 ≤ # buf2, n2 ≤ # buf2, (n0 + n2) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, ∀ n2, n3, n4, err, inode, m, md, boolvar, m0, m1, m2, isdir, dirs, files, buf, asynced. n2 - n3 + n4 < n5 → err = ESUCCESS ∧ inode = mkinode(m, md, boolvar, m0, m1, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ m2 ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err); while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err)⟫ true ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, ino1, inode, dirs, files, asynced; buf2, n2, isdir, err)⟫ true

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [VFS_PAGE_SIZE, (n0 + n2) % 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: VFS_PAGE_SIZE, (n0 + n2) % VFS_PAGE_SIZE, n