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Proof step 32 from proof abs-nodes-unique-weak-h (previous step)

lax0.head = @(m0, m1), abs-nodes(buf1 + buf0, m, x1, lax1, true), abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x, lax0, true) ∨ lax0 ≠ [] ∧ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m + # buf1, x, lax0.tail, true), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ nd ' + x = x1 ∧ lax0 = lax1

User applied rule constructor cut

And obtained the following new goals

Proof step 33:
lax0.head = @(m0, m1), x1 = [], abs-nodes(buf1 + buf0, m, x1, lax1, true), abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x, lax0, true) ∨ lax0 ≠ [] ∧ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m + # buf1, x, lax0.tail, true), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ nd ' + x = x1 ∧ lax0 = lax1
Proof step 42:
lax0.head = @(m0, m1), x1 = nd0 + x2, abs-nodes(buf1 + buf0, m, x1, lax1, true), abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x, lax0, true) ∨ lax0 ≠ [] ∧ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m + # buf1, x, lax0.tail, true), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ nd ' + x = x1 ∧ lax0 = lax1

Rule argument

var: x1

Additional information

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