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Proof step 16 from proof abs-nodes-add-crash-aligned-nodes (previous step)

# buf = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf2 + # buf = (y + a ').flashsize, abs-node(buf, a), abs-nodes(buf0, 0, x, lax, false), abs-nodes(buf2, # buf0, y, lax1, false) ⊦ abs-nodes((buf0 + buf2 + buf).align↓, 0, x + y + a ', lax + lax1 + @(# buf2 + # buf0, # buf) ', boolvar) ↔ is-aligned(# buf0 + # buf2 + # buf, EB_PAGE_SIZE)

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-add-crash-aligned seq: ⊦ abs-nodes(buf0, x, lax, false) ∧ abs-node(buf1, a) → ( abs-nodes ((buf0 + buf1).align↓, x + a ', lax + @(# buf0, a.flashsize) ', boolvar) ↔ is-aligned(# buf0 + # buf1, EB_PAGE_SIZE)) subst: [buf0, x, lax, buf1, a, boolvar] → [buf0 + buf2, x + y, lax + lax1, buf, a, boolvar]

Additional information

Used simplifier rules: abs-nodes: ⊦ abs-nodes(buf, x, lax, weak) ↔ abs-nodes(buf, 0, x, lax, weak);%abs-nodes-append-h: ⊦ abs-nodes(buf0, m, x0, lax0, false) → ( abs-nodes(buf0 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak));%abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);% ⊦ abs-node(buf, nd0) → (abs-node(buf, nd1) ↔ nd0 = nd1); (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: buf0 + buf2, x + y, lax + lax1, buf, a, boolvar