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Proof step 25 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n1 = (n2 + VFS_PAGE_SIZE) + n * VFS_PAGE_SIZE, n < m0, n1 < VFS_PAGE_SIZE, n1 < n2 + VFS_PAGE_SIZE ⊦ (m0 ∈ content ⊃ content[m0];zeropage)[n1] = ((n2 + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n ∈ content ⊃ content[(n2 + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n];zeropage)[n2 % VFS_PAGE_SIZE], m0 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ m < n ↔ (∃ m0. m + m0 = n ∧ m0 ≠ 0)
Proof step 27:
# buf = VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n1 = (n2 + VFS_PAGE_SIZE) + n * VFS_PAGE_SIZE, n1 < n2 + VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE, ∃ m1. n + m1 = m0 ∧ m1 ≠ 0 ⊦ (m0 ∈ content ⊃ content[m0];zeropage)[n1] = ((n2 + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n ∈ content ⊃ content[(n2 + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n];zeropage)[n2 % VFS_PAGE_SIZE], m0 = n

Rule argument

spec: nat-basic name: addex seq: ⊦ m < n ↔ (∃ m0. m + m0 = n ∧ m0 ≠ 0) subst: [n, m] → [m0, n] flags: <all paths>

Additional information

Used terms: m0, n