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Proof step 6 from proof abs-nodes-append-h (previous step)

abs-nodes(buf0, m, [], [], false), ∀ buf, m, x0, lax0, buf1, x1, lax1, weak. # buf < # buf0 → abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf, x1, lax1, weak)) ⊦ abs-nodes(buf0 + buf1, m, x1, lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 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 8:
# buf0 = 0 ∧ [] = [] ∨ (∃ buf2, buf1. buf0 = buf2 + buf1 ∧ abs-padding(buf2) ∧ abs-nodes(buf1, m + # buf2, [], [], false)) ∨ false ∧ abs-failed(buf0) ∧ [] = [], ∀ buf, m, x0, lax0, buf1, x1, lax1, weak. # buf < # buf0 → abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf, x1, lax1, weak)) ⊦ abs-nodes(buf0 + buf1, m, x1, lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

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] → [false, [], m, buf0] flags: <all paths>

Additional information

Used terms: false, [], m, buf0