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Proof step 46 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, lpt1[log1.last] = mklp(gstore[log1.last].ref-size, m1, LP_GROUP_NODES, m2), avol[log1.last] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), pstate = journal(log1.last), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, log1 ≠ [], log1.last < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore[log1.last]), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), log1.last ∈ gstore, istore0 ⊑ istore, ¬ dups(log1), ¬ log1.last ∈ ginval, isbuf1 → synced(avol) ⊦ ⟨apersistence_add_gnds#([], adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ log1.last = pstate.lnum ∧ [] = ax0 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
# lpt0 = # avol, # lpt1 = # avol, avol[log1.last] = mapped(buf), lpt1[log1.last] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[log1.last] = groupblock(gndx, lax, m0), keyset(gch) = gc-heap(lpt1, log1), pstate = journal(log1.last), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, log1.last < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(gstore[log1.last]), 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), log1.last ∈ gstore, istore0 ⊑ istore, isbuf1 → synced(avol) ⊦ ⟨apersistence_add_gnds#([], adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ log1.last = pstate.lnum ∧ [] = ax0 ∧ ESUCCESS = err0), log1 = [], dups(log1), log1.last ∈ ginval

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[log1.last], gndx, lax, m0]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[log1.last], gndx, lax, m0