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Proof step 22 from proof bin-heap-inv-cleanup-lpt (previous step)

lpt[m4] = mklp(m1, m2, lpf, m3), kar[lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[m4].gcheapidx] = key-index(natkey, m4), 2exp-size(# kar), m4 < # lpt, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[m4].gcheapidx < m, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[m4].gcheapidx < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m3 = lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[m4].gcheapidx

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
kar[m6] = key-index(natkey, m4), lpt[m4] = mklp(m1, m2, lpf, m3), lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[m4] = mklp(m0, m5, lpf0, m6), 2exp-size(# kar), m6 < # kar, m6 < m, m4 < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m3 = m6

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 .map (λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ) ) [m4 ], m0, m5, lpf0, m6]

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 .map (λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ) ) [m4 ], m0, m5, lpf0, m6