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Proof step 26 from proof inv-read (previous step)

of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), err = ESUCCESS, ino3 = 0, dom of < ino2, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, m0 ≤ m1, n ≤ # buf ⊦ ⟪vfs_read_loop#(m0, m0 + n, mkinode(m, md, false, m2, 0, m1), false, dirs, files, asynced; buf, ino3, err); if ino3 ≠ 0 then err := ESUCCESS; of[fd].pos := of[fd].pos + ino3; n := ino3⟫ (of-cons(of, dirs, files) ∧ dom of < ino2), mode ≠ MODE_R ∧ mode ≠ MODE_RW

User applied rule insert program lemma

And obtained the following new goals

Proof step 27:
n0 + n ≤ n1, inode.ino ∈ files, n0 + n ≤ inode.size, n1 - n0 ≤ # buf, afs-cons(dirs, files) ⊦ ⟪vfs_read_loop#(n0, n1, inode, bv, dirs, files, asynced; buf, n, err)⟫ true
Proof step 28:
bv0 ↔ false, asynced0 ↔ asynced, files[m] = mkfile(m1, md, m2, content), of[fd] = mkfile(m, mode, m0), dirs0 = dirs, err = ESUCCESS, files0 = files, ino3 = 0, inode0 = mkinode(m, md, false, m2, 0, m1), n2 = m0, n3 = m0 + n, dom of < ino2, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, mkinode(m, md, false, m2, 0, m1).ino ∈ files, n ≤ # buf, m0 ≤ m1, m0 + ino3 ≤ m0 + n, m0 + ino3 ≤ mkinode(m, md, false, m2, 0, m1).size, m0 + n - m0 ≤ # buf ⊦ [vfs_read_loop#(m0, m0 + n, mkinode(m, md, false, m2, 0, m1), false, dirs, files, asynced; buf, ino3, err)] (true → ⟪if ino3 ≠ 0 then err := ESUCCESS; of[fd].pos := of[fd].pos + ino3; n := ino3⟫ (of-cons(of, dirs, files) ∧ dom of < ino2)), mode ≠ MODE_R ∧ mode ≠ MODE_RW

Rule argument

spec: <toplevel> name: read-loop-term seq: n0 + n ≤ n1, inode.ino ∈ files, n0 + n ≤ inode.size, n1 - n0 ≤ # buf, afs-cons(dirs, files) ⊦ ⟪vfs_read_loop# (n0, n1, inode, bv, dirs, files, asynced; buf, n, err)⟫ true subst: [asynced, files, dirs, bv, inode, n1, n0, err, n, buf] → [asynced, files, dirs, false, mkinode(m, md, false, m2, 0, m1), m0 + n, m0, err, ino3, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ m + n - m = n; (s)