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Proof step 10 from proof abs-nodes-unique-weak-h (previous step)

abs-nodes(buf, m, x1, lax1, true), buf = mkbuf(0) ∨ buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], [], true) ∨ abs-failed(buf), ∀ buf0, m, x0, lax0, x1, lax1. # buf0 < # buf → abs-nodes(buf0, m, x0, lax0, true) ∧ abs-nodes(buf0, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ [] = x1 ∧ [] = lax1

User applied rule case distinction

And obtained the following new goals

Proof step 11:
buf = buf0 + buf1, abs-nodes(buf, m, x1, lax1, true), abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), ∀ buf0, m, x0, lax0, x1, lax1. # buf0 < # buf → abs-nodes(buf0, m, x0, lax0, true) ∧ abs-nodes(buf0, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ [] = x1 ∧ [] = lax1

Rule argument

pos: left 2

Additional information

Used simplifier rules: abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];%abs-failed-abs-nodes-h: ⊦ abs-failed(buf) → (abs-nodes(buf, n, x, lax, weak) ↔ lax = [] ∧ x = [] ∧ weak);