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Proof step 8 from proof refine-deallocate-gnd (previous step)

# lpt0 = # avol, # lpt = # avol, isbuf0 ↔ pstate = readonly, gstore[n] = groupblock(gndx, lax, m0), lpt[n] = mklp(m0, m1, LP_GROUP_NODES, m2), adr = adr0, keyset(gch) = gc-heap(lpt, log1), log = log1, log0 = log1, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n < # avol, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), 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(avol), n ∈ gstore0, n ∈ gstore, istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer ⊦ ⟪if synced(avol) ∧ n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log0 then let isbuf = ? in {awbuf_is_readonly#(adr, m, log, avol, lpt0, ns, bleb, isbuf0; ; isbuf); if isbuf then err := EROFS else {awbuf_unmap#(n, adr, m, log, lpt0, ns, bleb, isbuf0; avol); lpt[n].flags := LP_FREE; lpt[n].ref-size := 0; lpt[n].size := 0; freelist := freelist + n; gc_heap_remove#(lpt[n].gcheapidx; gch, lpt); err := ESUCCESS}} else abort⟫ ⟨apersistence_deallocate_gnd#(n, adr0, istore, istore0, gstore0, log1, m, ns0, pstate, true; ginval, gstore; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err0), dups(log1), n ∈ log1

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 9:
# lpt = # avol, # lpt0 = # avol, isbuf0 ↔ pstate = readonly, lpt[n] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m0), adr = adr0, keyset(gch) = gc-heap(lpt, log1), log = log1, log0 = log1, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, n < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), 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(avol), n ∈ gstore, n ∈ gstore0, istore0 ⊑ istore, pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ ⟪let isbuf = ? in {awbuf_is_readonly#(adr, m, log, avol, lpt0, ns, bleb, isbuf0; ; isbuf); if isbuf then err := EROFS else {awbuf_unmap#(n, adr, m, log, lpt0, ns, bleb, isbuf0; avol); lpt[n].flags := LP_FREE; lpt[n].ref-size := 0; lpt[n].size := 0; freelist := freelist + n; gc_heap_remove#(lpt[n].gcheapidx; gch, lpt); err := ESUCCESS}}⟫ ⟨apersistence_deallocate_gnd#(n, adr0, istore, istore0, gstore0, log1, m, ns0, pstate, true; ginval, gstore; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err0), dups(log1), n ∈ log1

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)