| # lpt0 = # avol, # lpt = # avol, isbuf0 ↔ pstate = readonly, avol0 = avol, bleb0 = bleb, freelist0 = freelist, gch0 = gch, keyset(gch) = gc-heap(lpt, log0), log0 = log0, log1 = log0, log2 = log0, lpt1 = lpt, lpt2 = lpt0, n = n0, n = n, n1 = n, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, 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, log0, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log0, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), istore0 ⊑ istore, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ [persistence_get_gc_block#(gch; n; err)] ( (err = ENOSPC ∨ err = ESUCCESS) ∧ (err ≠ ESUCCESS → n = n1) ∧ (err = ESUCCESS → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log1) → ⟨apersistence_get_gc_block#(adr0, istore, istore0, ginval, gstore, gstore0, log0, m, ns0, pstate, isbuf; n0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ n = n0 ∧ err = err0)), dups(log0) |
# lpt0 = # avol, # lpt = # avol, keyset(gch) = gc-heap(lpt, log0), n = n0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, 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, log0, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log0, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), istore0 ⊑ istore, ¬ dups(log0), pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ [persistence_get_gc_block#(gch; n; err)] ( (err = ENOSPC ∨ err = ESUCCESS) ∧ (err ≠ ESUCCESS → n = n0) ∧ (err = ESUCCESS → n < # avol ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log0) → ⟨apersistence_get_gc_block#(adr0, istore, istore0, ginval, gstore, gstore0, log0, m, ns0, pstate, isbuf; n0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ n = n0 ∧ err = err0))