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Proof step 114 from proof truncate-inv (previous step)

files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0 upto (m2 * VFS_PAGE_SIZE + n0))]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0 upto (m2 * VFS_PAGE_SIZE + n0))], ino4 ∈ files2 ⊦ ((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0, m2 ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 115:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 116:
files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0 upto (m2 * VFS_PAGE_SIZE + n0))]), afs-cons(dirs0, files2), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0 upto (m2 * VFS_PAGE_SIZE + n0))], ino4 ∈ files2 ⊦ n0 = 0, m2 ∈ content0, #(((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0) = # σ⊥ ∧ (∀ n. ⌜n⌝ < #(((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0) → (((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0)[n] = (σ⊥)[n])

Rule argument

spec: stream, inst: buffer-inf name: extensionality seq: ⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n]) subst: [σ2, σ] → [σ⊥, ( (content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0] flags: <all paths>

Additional information

Used terms: σ⊥, ( (content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0