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Proof step 5 from proof upto-same (previous step)

files[ino] = mkfile(m0, md0, m1, content0), ino ∈ files, ∀ n. n ∈ content0 → n * VFS_PAGE_SIZE < m0 ⊦ content0 upto m0 = content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 7:
files[ino] = mkfile(m0, md0, m1, content0), ino ∈ files, ∀ n. n ∈ content0 → n * VFS_PAGE_SIZE < m0 ⊦ ∀ n. (n ∈ content0 upto m0 ↔ n ∈ content0) ∧ (n ∈ content0 upto m0 → (content0 upto m0)[n] = content0[n])

Rule argument

spec: store, inst: file-content name: k-Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n])) subst: [content0, content] → [content0, content0 upto m0] flags: <all paths>

Additional information

Used terms: content0, content0 upto m0