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Proof step 117 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 ⊦ n0 = 0, m2 ∈ content0, #(((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] = zero

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ # σ0 = ∞ → #(σ0 from n) = ∞
Proof step 119:
#(((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥) = ∞, 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)[n] = zero

Rule argument

spec: stream, inst: buffer-inf name: inf-size-from seq: ⊦ # σ0 = ∞ → #(σ0 from n) = ∞ subst: [n, σ0] → [m2 * VFS_PAGE_SIZE + n0, ( (content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ # σ⊥ = ∞; (s)% ⊦ ⌜m⌝ + ∞ = ∞; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf] Used terms: m2 * VFS_PAGE_SIZE + n0, ((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥