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Proof step 6 from proof replay-lpt-at (previous step)

lpt[m] = mklp(m0, m1, lpf, m2), n0 < # lpt, m < # lpt, m ≤ n0, ∀ lpt, m, m0, m1, lpf, m2, nx. lpt[m] = mklp(m0, m1, lpf, m2) ∧ m < # lpt ∧ m < n0 ∧ n0 ≤ # lpt → replay-lpt(lpt, nx, n0)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) ) ⊦ (lpt[n0].flags = LP_FREE ∨ n0 ∈ nx ⊃ replay-lpt(lpt, nx, n0) ;(lpt[n0].flags = LP_INDEX_NODES ∧ lpt[n0].ref-size ≠ 0 ⊃ replay-lpt(lpt, nx, n0)[n0, lpt[n0].size:= LEB_SIZE] ;(lpt[n0].ref-size = 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, lpt[n0].gcheapidx)];replay-lpt(lpt, nx, n0)) ) ) [m ] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
lpt[m] = mklp(m0, m1, lpf, m2), lpt[n0] = mklp(m3, m4, lpf0, m5), m < # lpt, n0 < # lpt, m ≤ n0, ∀ lpt, m, m0, m1, lpf, m2, nx. lpt[m] = mklp(m0, m1, lpf, m2) ∧ m < # lpt ∧ m < n0 ∧ n0 ≤ # lpt → replay-lpt(lpt, nx, n0)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) ) ⊦ (lpf0 = LP_FREE ∨ n0 ∈ nx ⊃ replay-lpt(lpt, nx, n0) ;(lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ replay-lpt(lpt, nx, n0)[n0, lpt[n0].size:= LEB_SIZE] ;(m3 = 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)];replay-lpt(lpt, nx, n0)) ) ) [m ] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) )

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] → [lpt[n0], m2, m3, lpf0]

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[n0], m2, m3, lpf0