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Proof step 2 from proof valid-content-trunc (previous step)

ino ∈ files ⊦ valid-content(ino, files[ino, mkfile(n1, md, m1, content upto n1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ valid-content(ino, files) ↔ (∀ n. n ∈ files[ino].content → n * VFS_PAGE_SIZE < files[ino].size)

Rule argument

spec: afs-base name: valid-content seq: ⊦ valid-content(ino, files) ↔ (∀ n. n ∈ files[ino].content → n * VFS_PAGE_SIZE < files[ino].size) subst: [files, ino] → [files[ino, mkfile(n1, md, m1, content upto n1)], ino] flags: <all paths>

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: files[ino, mkfile(n1, md, m1, content upto n1)], ino