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Proof step 4 from proof abs-split-by-address-h (previous step)

abs-nodes(buf, m, x, lax0 + ladr ' + lax1, boolvar0), ∀ buf0, m, x, lax0, ladr, lax1, boolvar0. # buf0 < # buf → abs-nodes(buf0, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf2, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf0 = buf3 + buf1 + buf2 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf0, buf1, buf2, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf = buf0 + buf1 + buf2 ∧ ladr = @(m + # buf0, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
x = nd + x2, abs-nodes(buf, m, x, lax0 + ladr ' + lax1, boolvar0), ∀ buf0, m, x, lax0, ladr, lax1, boolvar0. # buf0 < # buf → abs-nodes(buf0, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf2, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf0 = buf3 + buf1 + buf2 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf0, buf1, buf2, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf = buf0 + buf1 + buf2 ∧ ladr = @(m + # buf0, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)

Rule argument

var: x

Additional information

Used simplifier rules: abs-nodes-elems-empty-adr-empty-h: ⊦ abs-nodes(buf, m, [], lax, weak) → lax = [];%list freely generated by [], +;;% ⊦ x + a ' + y ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ lax + lax0 = [] ↔ lax = [] ∧ lax0 = []; (as)% ⊦ ladr ' + lax ≠ []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]