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Proof step 32 from proof read-inv-rec (previous step)

# buf0 = # buf1, # buf1 = n4 + n + min(n3, n6, n1), n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, n + min(n3, n6, n1) ≤ # buf1, n3 + n ≤ # buf1, min(n3, n6, n1) + n ≤ # buf1 ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((content.stream from n0 + n) to n6 to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)) = ((content.stream from n0) to min(n3, n6, n1) + n) + (⌜buf0⌝ from min(n3, n6, n1) + n), n6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
¬ # σ0 < ⌜n⌝ ⊦ m ≤ n → σ0 to n to m = σ0 to m
Proof step 34:
# buf1 = n4 + n + min(n3, n6, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, min(n3, n6, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n6, n1) ≤ # buf1, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, min(n3, n6, n1) ≤ n6 ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)) = ((content.stream from n0) to min(n3, n6, n1) + n) + (⌜buf0⌝ from min(n3, n6, n1) + n), n6 = 0, #(content.stream from n0 + n) < ⌜n6⌝

Rule argument

spec: stream, inst: buffer-inf name: to-to-leq seq: ¬ # σ0 < ⌜n⌝ ⊦ m ≤ n → σ0 to n to m = σ0 to m subst: [m, n, σ0] → [min(n3, n6, n1), n6, content.stream from n0 + n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(content.stream from n) = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n1 < min(n0, n1, n2); (s) Used terms: min(n3, n6, n1), n6, content.stream from n0 + n