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Proof step 29 from proof bin-heap-inv-cleanup-lpt (previous step)

lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[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[kar[m0].idx].gcheapidx = m0 ⊦ kar[m0].idx < # lpt ∧ m3 = m0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[m4] = mklp(m1, m2, lpf, m3), kar[m0] = key-index(natkey, m4), 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[kar[m0].idx].gcheapidx = m0 ⊦ m4 < # lpt ∧ m3 = m0

Rule argument

spec: key-index, inst: gc-heap-rename-gc-heap-base name: elim seq: ⊦ natkey = ki.key ∧ m = ki.idx ↔ ki = key-index(natkey, m) subst: [ki, natkey, m] → [kar[m0], natkey, m4]

Additional information

Used simplifier rules: ⊦ natkey = ki.key ∧ m = ki.idx ↔ ki = key-index(natkey, m); (elim) Used terms: kar[m0], natkey, m4