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Proof step 15 from proof abs-nodes-no-padding-rec (previous step)

# buf1 + # buf0 = (2 * NODE_HEADER_SIZE + a.alignedsize) + x.flashsize, abs-nodes(buf0, m + # buf1, a ' + x, @(m0, m1) ' + lax0, false), abs-padding(buf1), ∀ buf2, a, x, m, m0, m1, lax0. # buf2 < #(buf1 + buf0) → # buf2 = (2 * NODE_HEADER_SIZE + a.alignedsize) + x.flashsize ∧ abs-nodes(buf2, m, a ' + x, @(m0, m1) ' + lax0, false) → (∃ buf3, buf1. buf2 = buf3 + buf1 ∧ m0 = m ∧ m1 = # buf3 ∧ abs-node(buf3, a) ∧ abs-nodes(buf1, m + # buf3, x, lax0, false)) ⊦ ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ m0 = m ∧ m1 = # buf3 ∧ abs-node(buf3, a) ∧ abs-nodes(buf2, m + # buf3, x, lax0, false)

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-at-least-flashsize seq: ⊦ abs-nodes(buf, m, x, lax, false) → # buf ≥ x.flashsize subst: [buf, m, x, lax] → [buf0, m + # buf1, a ' + x, @(m0, m1) ' + lax0]

Additional information

Used simplifier rules: abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);%size-rec: ⊦ (a ' + x).flashsize = a.flashsize + x.flashsize;% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ abs-padding(mkbuf(0)); (s) Used terms: buf0, m + # buf1, a ' + x, @(m0, m1) ' + lax0