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

abs-nodes(buf, m, x0 + x1, lax, weak), ∀ buf0, m, x0, x1, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, x0 + x1, lax, weak) → (∃ buf2, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf0 = buf2 + buf1 ∧ abs-nodes(buf2, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf2, x1, lax1, weak)) ⊦ ∃ buf0, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf = buf0 + buf1 ∧ abs-nodes(buf0, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
x0 = [], abs-nodes(buf, m, x0 + x1, lax, weak), ∀ buf0, m, x0, x1, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, x0 + x1, lax, weak) → (∃ buf2, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf0 = buf2 + buf1 ∧ abs-nodes(buf2, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf2, x1, lax1, weak)) ⊦ ∃ buf0, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf = buf0 + buf1 ∧ abs-nodes(buf0, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf0, x1, lax1, weak)
Proof step 7:
x0 = nd + x, abs-nodes(buf, m, x0 + x1, lax, weak), ∀ buf0, m, x0, x1, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, x0 + x1, lax, weak) → (∃ buf2, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf0 = buf2 + buf1 ∧ abs-nodes(buf2, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf2, x1, lax1, weak)) ⊦ ∃ buf0, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf = buf0 + buf1 ∧ abs-nodes(buf0, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

Rule argument

var: x0

Additional information

Used simplifier rules: list freely generated by [], +;;