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Proof step 141 from proof refine-allocate-gnd (previous step)

# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), err = err0, keyset(gch) = gc-heap(lpt, log1), log0 = log1, lpt1 = lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)] [n0, lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)][n0].ref-size:= 0 ], pstate0 = pstate, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # lpt, n0 < # lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)], n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨apersistence_allocate_gnd#(adr0, istore, istore0, gstore0, m, ns0, true; ginval, gstore, log1, pstate; err1)⟩ ( abs-istore(avol0[n0, mapped(mkbuf(0))], lpt1, istore) ∧ abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt1, gstore, ginval) ∧ log1 = log0 ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err1), n0 ' + nx0 = [], err = ESUCCESS, pstate = readonly, dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 142:
# lpt0 = # avol0, # lpt = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), keyset(gch) = gc-heap(lpt, log1), log0 = log1, pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate ≠ readonly, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), istore0 ⊑ istore, ⌊err0⌋ , ¬ dups(log1), pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer ⊦ ⟨apersistence_allocate_gnd#(adr0, istore, istore0, gstore0, m, ns0, true; ginval, gstore, log1, pstate; err1)⟩ ( abs-gstore(avol0, lpt, gstore, ginval) ∧ log1 = log0 ∧ ginval < # avol0 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err0 = err1)

Rule argument

Additional information

Used simplifier rules: freelist-cons-first-free: ⊦ freelist-cons(lpt, n ' + freelist) → n < # lpt ∧ lpt[n].flags = LP_FREE; (forward) from specification persistence-base%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lpf ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-gstore(avol[n, aleb], lpt, gstore, ginval) ↔ abs-gstore(avol, lpt, gstore, ginval)); (s)%lpf ≠ LP_GROUP_NODES, lp.flags ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-gstore(avol, lpt[n, lp], gstore, ginval) ↔ abs-gstore(avol, lpt, gstore, ginval)); (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%lpf ≠ LP_INDEX_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-istore(avol[n, aleb], lpt, istore) ↔ abs-istore(avol, lpt, istore)); (s)%lpf ≠ LP_INDEX_NODES, lp.flags ≠ LP_INDEX_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-istore(avol, lpt[n, lp], istore) ↔ abs-istore(avol, lpt, istore)); (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_FREE ≠ LP_INDEX_NODES; (s)%m < # lpt ⊦ lpt[m, lp][m, lp0] = lpt[m, lp0]; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mklp(m, m0, lpf, m1).ref-size:= m2 = mklp(m2, m0, lpf, m1); (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ # lpt[n, lp] = # lpt; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ' + nx ≠ []; (s)