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Proof step 97 from proof truncate-greater (previous step)

files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n0 ≠ 0, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0 upto m3).stream to n0 + m3 = (content0.stream to m3) + (σ⊥ to n0)), m3 % VFS_PAGE_SIZE ≠ 0 ∧ m3 / VFS_PAGE_SIZE ∈ content0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 98:
files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), m3 = m1 * VFS_PAGE_SIZE + n1, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0 upto m3).stream to n0 + m3 = (content0.stream to m3) + (σ⊥ to n0)), VFS_PAGE_SIZE = 0, n0 = 0, n1 ≠ 0 ∧ m1 ∈ content0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [n, m, m0, n0] → [VFS_PAGE_SIZE, m3, m1, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: VFS_PAGE_SIZE, m3, m1, n