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Proof step 70 from proof read-loop-term (previous step)

VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, # links(m, dirs), content), buf1 = copy(zeropage, (n0 + n6) % VFS_PAGE_SIZE, buf, n6, min(n5, n7, n8)), err = ESUCCESS, inode = mkinode(m, md, boolvar, m0, m1, n8 + n0 + n6), ¬ isdir, n = n6 + min(n5, n7, n8), n1 = n5 + n0 + n6, afs-cons(dirs, files), m ∈ files, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7, n8) ≤ VFS_PAGE_SIZE, n6 + min(n5, n7, n8) ≤ # buf, n6 ≤ # buf, n5 + n6 ≤ # buf, ∀ 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 ⊦ ⟪vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err); while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err)⟫ true, n5 = 0, n7 = 0, n8 = 0, (n0 + n6) / VFS_PAGE_SIZE ∈ content

User applied rule apply induction

And obtained the following new goals

Proof step 71:
⟪vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err); n3 := n0, n2 := n1, buf := buf1, n4 := n; while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err)⟫ true, VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, # links(m, dirs), content), buf1 = copy(zeropage, (n0 + n6) % VFS_PAGE_SIZE, buf, n6, min(n5, n7, n8)), err = ESUCCESS, inode = mkinode(m, md, boolvar, m0, m1, n8 + n0 + n6), ¬ isdir, n = n6 + min(n5, n7, n8), n1 = n5 + n0 + n6, afs-cons(dirs, files), m ∈ files, n5 + n6 ≤ # buf, n6 ≤ # buf, n6 + min(n5, n7, n8) ≤ # buf, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7, n8) ≤ 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 ⊦ ⟪vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err); while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err)⟫ true, n5 = 0, n7 = 0, n8 = 0, (n0 + n6) / VFS_PAGE_SIZE ∈ content

Rule argument

subst: [n2, n3, n4, err, inode, m, md, boolvar, m0, m1, m2, isdir, dirs, files, buf, asynced] → [n1, n0, n, err, inode, m, md, boolvar, m0, m1, n8 + n0 + n6, isdir, dirs, files, buf1, asynced]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n2 < min(n0, n1, n2); (s)% ⊦ ¬ n0 < min(n0, n1, n2); (s)% ⊦ m + n - n + n1 = m - n1; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ min(n0, n1, n2) = 0 ↔ n0 = 0 ∨ n1 = 0 ∨ n2 = 0; (ws) Used terms: n1, n0, n, err, inode, m, md, boolvar, m0, m1, n8 + n0 + n6, isdir, dirs, files, buf1, asynced