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Proof step 18 from proof bin-heap-inv-cleanup-lpt (previous step)

2exp-size(# kar), m0 < m, m0 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ m0. m0 < m → kar[m0].idx < # lpt ∧ lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[kar[m0].idx].gcheapidx = m0 ⊦ kar[m0].idx < # lpt ∧ lpt[kar[m0].idx].gcheapidx = m0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
lpt[kar[m0].idx] = mklp(m1, m2, lpf, m3), 2exp-size(# kar), m0 < # kar, m0 < m, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ m0. m0 < m → kar[m0].idx < # lpt ∧ lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[kar[m0].idx].gcheapidx = m0 ⊦ kar[m0].idx < # lpt ∧ m3 = m0

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[kar[m0].idx], m1, m2, lpf, m3]

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[kar[m0].idx], m1, m2, lpf, m3