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Proof step 197 from proof refine-allocate-gnd (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, lpt1[n0] = mklp(0, m1, LP_FREE, m2), avol = avol0[n0, unmapped], err = err0, freelist = n0 ' + nx0, keyset(gch) = gc-heap(lpt1, log1), log = log1, log0 = log1, n = n0, pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol0), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, 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, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨apersistence_allocate_gnd#(adr0, istore, istore0, gstore0, m, ns0, true; ginval, gstore, log1, pstate; err1)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ log1 = log0 ∧ ginval < # lpt1 ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err1), err = ESUCCESS, pstate = readonly, dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 198:
# lpt0 = # avol0, # lpt1 = # avol0, lpt1[n0] = mklp(0, m1, LP_FREE, m2), keyset(gch) = gc-heap(lpt1, log1), log = log1, pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate ≠ readonly, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol0), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, 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, lpt1, gstore, ginval) ∧ log1 = log ∧ 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: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ synced(avol) → synced(avol[n, unmapped]); (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)% ⊦ 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)% ⊦ LP_FREE ≠ LP_INDEX_NODES; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)