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Proof step 21 from proof lpt-ram-flash-write-same (previous step)

# lpt0 = # lpt, lpt[n] = mklp(n0, m, lpf, n2), lpt[n, mklp(m0, m, lpf, m2)][n1] = mklp(m1, m3, LP_GROUP_NODES, m4), lpt0[n1] = mklp(m5, m6, LP_GROUP_NODES, m7), n1 < # lpt, n < # lpt, lpt[n1].flags = LP_GROUP_NODES → lpt[n1].size = m6 ⊦ m3 = m6, n1 ∈ nx

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# lpt0 = # lpt, lpt0[n1] = mklp(m5, m6, LP_GROUP_NODES, m7), lpt[n, mklp(m0, m, lpf, m2)][n1] = mklp(m1, m3, LP_GROUP_NODES, m4), lpt[n] = mklp(n0, m, lpf, n2), lpt[n1] = mklp(m8, m9, lpf0, m10), n < # lpt, n1 < # lpt, lpf0 = LP_GROUP_NODES → m9 = m6 ⊦ m3 = m6, n1 ∈ nx

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n1], m8, m9, lpf0, m10]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n1], m8, m9, lpf0, m10