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Proof step 39 from proof refine-deallocate-gnd (previous step)

# lpt2 = # avol, # lpt0 = # avol, key-index(m3, n) ∈ gc-heap(lpt2, log1) ↔ n < # lpt2 ∧ ¬ n ∈ log1 ∧ lpt2[n].ref-size = m3 ∧ lpt2[n].flags = LP_GROUP_NODES, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m3), keyset(gch) = gc-heap(lpt2, log1), lpt1 = lpt2[n, mklp(0, 0, LP_FREE, m2)], remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n < # avol, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), n ∈ gstore, n ∈ gstore0, istore0 ⊑ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ ⟪gc_heap_remove#(lpt1[n].gcheapidx; gch, lpt1); err := ESUCCESS⟫ ⟨apersistence_deallocate_gnd#(n, adr0, istore, istore0, gstore0, log1, m, ns0, pstate, true; ginval, gstore; err0)⟩ ( abs-istore(avol[n, unmapped], lpt1, istore) ∧ abs-gstore(avol[n, unmapped], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered → bleb = buffered(pstate.lnum)) ∧ err = err0), buffered(n) = bleb, pstate = readonly, dups(log1), n ∈ log1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# lpt0 = # avol, # lpt2 = # avol, gstore[n] = groupblock(gndx, lax, m3), lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt2, log1), lpt1 = lpt2[n, mklp(0, 0, LP_FREE, m2)], remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, # gc-heap(lpt2, log1) ≠ 0, buffered(n) ≠ bleb, gc-heap(lpt2, log1) ≠ ∅, pstate ≠ readonly, ginval < # avol, n < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), 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(avol), key-index(m3, n) ∈ gc-heap(lpt2, log1), n ∈ gstore0, n ∈ gstore, istore0 ⊑ istore, ¬ dups(log1), ¬ n ∈ log1, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered → bleb = buffered(pstate.lnum) ⊦ ⟪gc_heap_remove#(lpt1[n].gcheapidx; gch, lpt1); err := ESUCCESS⟫ ⟨apersistence_deallocate_gnd#(n, adr0, istore, istore0, gstore0, log1, m, ns0, pstate, true; ginval, gstore; err0)⟩ ( abs-istore(avol[n, unmapped], lpt1, istore) ∧ abs-gstore(avol[n, unmapped], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered → bleb = buffered(pstate.lnum)) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ gchs ≠ ∅ → # gchs ≠ 0; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%ne-01: ⊦ ki ∈ gchs → gchs ≠ ∅; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)