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Proof step 8 from proof valid-content-reduce (previous step)

files1[ino] = mkfile(m, md, m0, content), valid-content(files1), n ∈ content, ino ∈ files1, m ≤ n * VFS_PAGE_SIZE, ino ∈ files0 ∧ n ∈ files0[ino].content → n * VFS_PAGE_SIZE < files0[ino].size, ∀ ino. ino ∈ files0 → valid-content(ino, files0) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
files1[ino] = mkfile(m, md, m0, content), files0[ino] = mkfile(m1, md0, m2, content0), valid-content(files1), ino ∈ files1, n ∈ content, m ≤ n * VFS_PAGE_SIZE, ino ∈ files0 ∧ n ∈ content0 → n * VFS_PAGE_SIZE < m1, ∀ ino. ino ∈ files0 → valid-content(ino, files0) ⊦

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] → [files0[ino], m1, md0, m2, content0]

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: files0[ino], m1, md0, m2, content0