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Proof step 9 from proof bufs-log-only-id-idx (previous step)

lpt0[nx.last] = mklp(m6, m7, lpf1, m8), lpt1[nx.last] = mklp(m0, m1, lpf, m2), lpt1[m] = mklp(m3, m4, lpf0, m5), lpt0[m] = mklp(m9, m10, lpf2, m11), id-idx(lpt0, lpt1) ⊦ m < # lpt1 ∧ (nx ≠ [] ∧ m = nx.last ∧ lpf = LP_GROUP_NODES ∨ lpf0 = LP_INDEX_NODES) ↔ m < # lpt0 ∧ (nx ≠ [] ∧ m = nx.last ∧ lpf1 = LP_GROUP_NODES ∨ lpf2 = LP_INDEX_NODES)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags)
Proof step 11:
# lpt1 = # lpt0, lpt0[m] = mklp(m9, m10, lpf2, m11), lpt1[m] = mklp(m3, m4, lpf0, m5), lpt1[nx.last] = mklp(m0, m1, lpf, m2), lpt0[nx.last] = mklp(m6, m7, lpf1, m8), ∀ n. n < # lpt1 → lpt0[n].ref-size = lpt1[n].ref-size ∧ lpt0[n].size = lpt1[n].size ∧ lpt0[n].flags = lpt1[n].flags ⊦ m < # lpt1 ∧ (nx ≠ [] ∧ m = nx.last ∧ lpf = LP_GROUP_NODES ∨ lpf0 = LP_INDEX_NODES) ↔ m < # lpt0 ∧ (nx ≠ [] ∧ m = nx.last ∧ lpf1 = LP_GROUP_NODES ∨ lpf2 = LP_INDEX_NODES)

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt1, lpt0] flags: <all paths>

Additional information

Used terms: lpt1, lpt0