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Proof step 1 from proof align-down-elim (conclusion)

⊦ buf0 = buf.align↓ ↔ (∃ buf1. buf = buf0 + buf1 ∧ # buf1 < EB_PAGE_SIZE ∧ is-aligned(# buf0, EB_PAGE_SIZE))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ ∃ buf1. buf = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE)) + buf1 ∧ # buf1 < EB_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: down-arrow-buf: ⊦ buf.align↓ = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE));%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%n ≠ 0 ⊦ m < n → align↓(m, n) = 0; (s)%n ≠ 0 ⊦ is-aligned(n0, n) → align↓(n0 + n1, n) = n0 + align↓(n1, n); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%m ≠ 0 ⊦ is-aligned(align↓(n, m), m); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)