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Proof step 3 from proof truncate-inv (previous step)

files1[ino].size = n, buf-opt = none, files0 = files1, inode = mkinode(ino, files1[ino].meta, false, files1[ino].nlink, 0, files1[ino].size), mkinode(ino, files1[ino].meta, false, files1[ino].nlink, 0, files1[ino].size) = inode0, afs-cons(dirs, files1), ino ∈ files1 ⊦ [afs_truncate#(files1[ino].size, files1[ino].size / VFS_PAGE_SIZE; buf-opt, inode, bv, err, dirs, files1, asynced)] ( (err = ESUCCESS ⊃ files1[ino].content.stream from n = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv(n0, n0 + n1, inode0, buf, 0, dirs, files1, files1)) ∧ files0 -- ino = files1 -- ino ;⌊err⌋ ) ∧ files0 ~ files1 ∧ inode = inode0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
files1[ino] = mkfile(m, md, m0, content), buf-opt = none, files0 = files1, inode = mkinode(ino, md, false, m0, 0, m), m = n, mkinode(ino, md, false, m0, 0, m) = inode0, afs-cons(dirs, files1), ino ∈ files1 ⊦ [afs_truncate#(m, m / VFS_PAGE_SIZE; buf-opt, inode, bv, err, dirs, files1, asynced)] ( (err = ESUCCESS ⊃ files1[ino].content.stream from n = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv(n0, n0 + n1, inode0, buf, 0, dirs, files1, files1)) ∧ files0 -- ino = files1 -- ino ;⌊err⌋ ) ∧ files0 ~ files1 ∧ inode = inode0)

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] → [files1[ino], m, md, m0, 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: files1[ino], m, md, m0, content