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Proof step 1 from proof align-down-app-same (conclusion)

⊦ (buf0 + buf1).align↓ = buf0.align↓ ↔ # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ subarray(buf0 + buf1, 0, align↓(# buf0 + # buf1, EB_PAGE_SIZE)) = subarray(buf0, 0, align↓(# buf0, EB_PAGE_SIZE)) ↔ # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: down-arrow-buf: ⊦ buf.align↓ = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE));%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)