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Proof step 6 from proof abs-nodes-no-padding-one (previous step)

# buf = (a ' + []).flashsize ⊦ abs-nodes(buf, m, a ' + [], lax, false) ↔ lax = @(m, # buf) ' ∧ abs-node(buf, a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ # buf = (a ' + x).flashsize → ( abs-nodes(buf, m, a ' + x, lax, false) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, false)))
Proof step 8:
# buf = (a ' + []).flashsize ⊦ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], lax.tail, false)) ↔ lax = @(m, # buf) ' ∧ abs-node(buf, a)

Rule argument

spec: <toplevel> name: abs-nodes-no-padding-rec seq: ⊦ # buf = (a ' + x).flashsize → ( abs-nodes(buf, m, a ' + x, lax, false) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, false))) subst: [lax, x, a, m, buf] → [lax, [], a, m, buf] flags: <all paths>

Additional information

Used terms: lax, [], a, m, buf