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Proof step 5 from proof replay-lpt-at (previous step)

lpt[m] = mklp(m0, m1, lpf, m2), m < n0 +1, m < # lpt, n0 +1 ≤ # lpt, ∀ 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))) ) ⊦ replay-lpt(lpt, nx, n0 +1)[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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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))) )

Rule argument

Additional information

Used simplifier rules: replay-lpt-rec: n < # lpt ⊦ replay-lpt(lpt, nx, n + 1) = (lpt[n].flags = LP_FREE ∨ n ∈ nx ⊃ replay-lpt(lpt, nx, n) ;(lpt[n].flags = LP_INDEX_NODES ∧ lpt[n].ref-size ≠ 0 ⊃ replay-lpt(lpt, nx, n)[n, lpt[n].size:= LEB_SIZE] ;(lpt[n].ref-size = 0 ⊃ replay-lpt(lpt, nx, n) [n, mklp(0, 0, LP_FREE, lpt[n].gcheapidx) ] ;replay-lpt(lpt, nx, n) ) ) );% ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m +1 = m + 1; (s)