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Proof step 15 from proof lpt-ram-flash-write-same (previous step)

# lpt0 = # lpt, lpt[n, mklp(m0, m, lpf, m2)][n1].flags = LP_GROUP_NODES, lpt0[n1].flags = LP_GROUP_NODES, lpt[n] = mklp(n0, m, lpf, n2), n < # lpt, n1 < # lpt, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_GROUP_NODES ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ nx → lpt[n].size = lpt0[n].size ⊦ lpt[n, mklp(m0, m, lpf, m2)][n1].size = lpt0[n1].size, n1 ∈ nx

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
# lpt0 = # lpt, lpt0[n1].flags = LP_GROUP_NODES, lpt[n] = mklp(n0, m, lpf, n2), lpt[n, mklp(m0, m, lpf, m2)][n1] = mklp(m1, m3, lpf0, m4), lpf0 = LP_GROUP_NODES, n1 < # 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 ⊦ m3 = lpt0[n1].size, 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[n, mklp(m0, m, lpf, m2)][n1], m1, m3, lpf0, m4]

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[n, mklp(m0, m, lpf, m2)][n1], m1, m3, lpf0, m4