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Proof step 2 from proof page-size-simp4 (previous step)

LEB_SIZE = n0 + n1 + EB_PAGE_SIZE, is-aligned(n1, EB_PAGE_SIZE) ⊦ n0 % EB_PAGE_SIZE = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
m ≠ 0 ⊦ is-aligned(n0, m) ∧ ¬ is-aligned(n1, m) → n0 ≠ n1
Proof step 4:
⊦ EB_PAGE_SIZE ≠ 0
Proof step 5:
⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE)

Rule argument

spec: align name: is-aligned-intro seq: m ≠ 0 ⊦ is-aligned(n0, m) ∧ ¬ is-aligned(n1, m) → n0 ≠ n1 subst: [m, n1, n0] → [EB_PAGE_SIZE, n0 + n1 + EB_PAGE_SIZE, LEB_SIZE] flags: <all paths>

Additional information

Used simplifier rules: page-size: ⊦ EB_PAGE_SIZE ≠ 0;%lebsize-page-size-is-aligned: ⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE);%n ≠ 0 ⊦ is-aligned(n, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s) Used terms: EB_PAGE_SIZE, n0 + n1 + EB_PAGE_SIZE, LEB_SIZE