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Proof step 87 from proof refine-allocate-ind (previous step)

# lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m5, LP_FREE, m6), err = ESUCCESS, err = err0, err2 = err, keyset(gch) = gc-heap(lpt2, log1), lpt1 = lpt2[n0, mklp(0, 0, LP_FREE, m6)][n0, lpt2[n0, mklp(0, 0, LP_FREE, m6)][n0].ref-size:= 0], pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, n0 < # lpt2[n0, mklp(0, 0, LP_FREE, m6)], n0 < # lpt2, n0 < # lpt1, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, 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, bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, ⌊err0⌋ ∨ err0 = ESUCCESS, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ ⟨apersistence_allocate_ind#(adr0, istore0, ginval, gstore, gstore0, log1, m, ns0, true; istore, pstate; err1)⟩ ( abs-istore(avol0[n0, mapped(mkbuf(0))], lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], istore) ∧ abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], gstore, ginval) ∧ ginval < # lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES] ∧ (pstate = unbuffered → buffered(n0) = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → buffered(n0) = buffered(pstate.lnum)) ∧ err2 = err1), bleb = buffered(n0), pstate = readonly, dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
# lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m5, LP_FREE, m6), keyset(gch) = gc-heap(lpt2, log1), pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, bleb ≠ buffered(n0), pstate ≠ readonly, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, ¬ 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, bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ ⟨apersistence_allocate_ind#(adr0, istore0, ginval, gstore, gstore0, log1, m, ns0, true; istore, pstate; err1)⟩ ( abs-istore(avol0[n0, mapped(mkbuf(0))], lpt2[n0, mklp(0, 0, LP_INDEX_NODES, m6)], istore) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ readonly → n0 = pstate.lnum) ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)%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_GROUP_NODES ≠ LP_INDEX_NODES; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)% ⊦ mklp(m, m0, lpf, m1).flags:= lpf0 = mklp(m, m0, lpf0, m1); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ # lpt[n, lp] = # lpt; (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)