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Proof step 8 from proof lpt-ram-flash-write-log-buf (previous step)

# lpt0 = # lpt, lpt0[n3] = mklp(m8, m9, LP_GROUP_NODES, m10), lpt[n, mklp(m0, m1, lpf, m2)][n3] = mklp(m5, m6, LP_GROUP_NODES, m7), lpt[n] = mklp(n0, n1, lpf, n2), lpt[nx.last] = mklp(m, m3, lpf0, m4), n < # lpt, n3 < # lpt, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_GROUP_NODES ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ nx → lpt[n].size = lpt0[n].size, nx ≠ [] ∧ n = nx.last ∧ lpf0 = LP_GROUP_NODES ∨ lpf = LP_INDEX_NODES ⊦ m6 = m9, n3 ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m ≠ n → lpt[n, lp][m] = lpt[m]
Proof step 10:
# lpt0 = # lpt, lpt[nx.last] = mklp(m, m3, lpf0, m4), lpt[n] = mklp(n0, n1, lpf, n2), lpt[n3] = mklp(m5, m6, LP_GROUP_NODES, m7), lpt0[n3] = mklp(m8, m9, LP_GROUP_NODES, m10), n3 < # lpt, n < # lpt, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_GROUP_NODES ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ nx → lpt[n].size = lpt0[n].size, nx ≠ [] ∧ n = nx.last ∧ lpf0 = LP_GROUP_NODES ∨ lpf = LP_INDEX_NODES ⊦ m6 = m9, n3 = n, n3 ∈ nx

Rule argument

spec: array, inst: gc-heap-base-index-array-base name: Put-other seq: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m] subst: [m, lp, n, lpt] → [n3, mklp(m0, m1, lpf, m2), n, lpt] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)% ⊦ nx.last = n ∧ nx ≠ [] → n ∈ nx; (s) Used terms: n3, mklp(m0, m1, lpf, m2), n, lpt