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Proof step 40 from proof prepost-replay-lpt (previous step)

# avol1 = n2 + n0, # lpt4 = n2 + n0, # avol = n2 + n0, lpt4[n0] = mklp(0, m1, lpf, m2), bleb = nobuffer, lpt = lpt0, m0 = n0, m0 < # avol, avol-replay-lpt-unchanged(avol1, avol, lpt4, log0), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), synced(avol), synced(avol1) ⊦ lpf = LP_FREE, lpf = LP_INDEX_NODES, n2 = 0, n0 ∈ log0, n0 + 1 ≤ # avol1 ∧ awbuf-inv(avol[m0, unmapped], nobuffer) ∧ replay-lpt(lpt4, log0, n0)[n0, mklp(0, 0, LP_FREE, m2)] = replay-lpt(lpt4, log0, n0 + 1) ∧ avol-replay-lpt-unchanged(avol1, avol[m0, unmapped], lpt4, log0) ∧ # avol1 < n2 + n0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);%elim-lp-upd-size: ⊦ lp.size:= n = mklp(lp.ref-size, n, lp.flags, lp.gcheapidx);% ⊦ ¬ n < n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%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) ) ) ); (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic