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Proof step 34 from proof abs-nodes-unique-weak-h (previous step)

lax0.head = @(m0, m1), abs-nodes(buf1 + buf0, m, [], [], 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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ abs-nodes(buf, m, [], lax, weak) ↔ # buf = 0 ∧ lax = [] ∨ (∃ buf0, buf1. buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], lax, weak)) ∨ weak ∧ abs-failed(buf) ∧ lax = []
Proof step 36:
lax0.head = @(m0, m1), 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), #(buf1 + buf0) = 0 ∧ [] = [] ∨ (∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ abs-padding(buf3) ∧ abs-nodes(buf2, m + # buf3, [], [], true)) ∨ true ∧ abs-failed(buf1 + buf0) ∧ [] = [], ∀ 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 ⊦

Rule argument

spec: <toplevel> name: abs-nodes-base seq: ⊦ abs-nodes(buf, m, [], lax, weak) ↔ # buf = 0 ∧ lax = [] ∨ (∃ buf0, buf1. buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], lax, weak)) ∨ weak ∧ abs-failed(buf) ∧ lax = [] subst: [weak, lax, m, buf] → [true, [], m, buf1 + buf0] flags: <all paths>

Additional information

Used terms: true, [], m, buf1 + buf0