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Proof step 14 from proof refine-set-gblock-refsize (previous step)

# lpt1 = # avol, # lpt0 = # avol, key-index(m1, m) ∈ gc-heap(lpt1, log0) ↔ m < # lpt1 ∧ ¬ m ∈ log0 ∧ lpt1[m].ref-size = m1 ∧ lpt1[m].flags = LP_GROUP_NODES, lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx, lax, m1), keyset(gch) = gc-heap(lpt1, log0), lpt = lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, m < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), m ∈ gstore0, m ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ ⟪gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)⟫ ⟨apersistence_set_gblock_refsize#(m, n, adr0, istore, istore0, ginval, gstore0, log0, m0, ns0, pstate, isbuf; gstore)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))), dups(log0), m ∈ log0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# lpt0 = # avol, # lpt1 = # avol, gstore[m] = groupblock(gndx, lax, m1), lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), keyset(gch) = gc-heap(lpt1, log0), lpt = lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, # gc-heap(lpt1, log0) ≠ 0, gc-heap(lpt1, log0) ≠ ∅, ginval < # avol, m < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), key-index(m1, m) ∈ gc-heap(lpt1, log0), m ∈ gstore, m ∈ gstore0, istore0 ⊑ istore, ¬ dups(log0), ¬ m ∈ 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) ⊦ ⟪gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)⟫ ⟨apersistence_set_gblock_refsize#(m, n, adr0, istore, istore0, ginval, gstore0, log0, m0, ns0, pstate, isbuf; gstore)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)))

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)