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Proof step 10 from proof truncate-greater (previous step)

files0 = files, inode = mkinode(m0, md, false, files[m0].nlink, 0, m3), old_ino = 0, old_ino0 = 0, m3 < n, afs-cons(dirs, files), m0 ∈ files ⊦ [buf-opt := none; afs_truncate_internal#(n, m3 / VFS_PAGE_SIZE; inode, buf-opt, old_ino0, old_ino, asynced0, err, dirs, files; asynced)] (err = ESUCCESS ⊃ files[inode.ino].content.stream to files[inode.ino].size = (files0[inode.ino].content.stream to m3) + (σ⊥ to (files[inode.ino].size - m3)) ∧ inode.ino ∈ files ∧ n = files[inode.ino].size ∧ files0[inode.ino].nlink = files[inode.ino].nlink ∧ files0 -- inode.ino = files -- inode.ino ;⌊err⌋ ∧ files0 = files )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
files[m0] = mkfile(m, md0, m1, content), files0 = files, inode = mkinode(m0, md, false, m1, 0, m3), old_ino = 0, old_ino0 = 0, m3 < n, afs-cons(dirs, files), m0 ∈ files ⊦ [buf-opt := none; afs_truncate_internal#(n, m3 / VFS_PAGE_SIZE; inode, buf-opt, old_ino0, old_ino, asynced0, err, dirs, files; asynced)] (err = ESUCCESS ⊃ files[inode.ino].content.stream to files[inode.ino].size = (files0[inode.ino].content.stream to m3) + (σ⊥ to (files[inode.ino].size - m3)) ∧ inode.ino ∈ files ∧ n = files[inode.ino].size ∧ files0[inode.ino].nlink = files[inode.ino].nlink ∧ files0 -- inode.ino = files -- inode.ino ;⌊err⌋ ∧ files0 = files )

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m0], m, md0, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m0], m, md0, m1, content