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Proof step 78 from proof refine-commit (previous step)

# lpt2 = # avol, # lpt0 = # avol, keyset(gch) = gc-heap(lpt2, log1), log0 = log1, lpt1 = lpt2, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, dom remove-refsize0(gstore) ∩ ginval = ∅, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate ≠ readonly, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, nobuffer), awbuf-inv(avol, bleb0), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, 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(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), istore0 ⊑ istore, ¬ dups(log1), pstate = unbuffered → bleb0 = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum) ⊦ [persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr2, m2, [], lpt1, ns2, nobuffer, false; lpt2, freelist, gch, avol)] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = [] ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, []) ∧ # lpt2 = # avol ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, []) ∧ awbuf-inv(avol, nobuffer) ∧ # lpt1 = # avol → ⟨ns1 := ns2; apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr2 ∧ maxino = m2 ∧ log1 = [] ∧ ginval < # lpt2 ∧ ns4 = ns1 ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ pstate = unbuffered ∧ ns0 = ns2 ∧ ESUCCESS = err1))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: persistence-asm name: prepost-gcheap-add-log seq: bin-heap-inv(gch, lpt), keyset(gch) = gc-heap(lpt, nx), lpt0 = lpt, ¬ dups(nx), ∀ n. n ∈ nx → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ ⟪persistence_gc_heap_add_log#(; nx, lpt, gch)⟫ ( nx = [] ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, nx) ∧ id-idx(lpt0, lpt)) subst: [gch, lpt, nx, lpt0] → [gch, lpt2, log0, lpt2] flags: <all paths>

Additional information

Used simplifier rules: fwd-in-gstore-lpt: ⊦ n ∈ gstore ∧ abs-gstore(avol, lpt, gstore, ginval) → n < # lpt ∧ lpt[n].ref-size = gstore[n].ref-size ∧ lpt[n].flags = LP_GROUP_NODES;%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%elems-in-notin-ginval: ⊦ n ∈ nx ∧ elems nx ∩ ns = ∅ → ¬ n ∈ ns; (forward) from specification apersistence-base%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%fwd-in-log-in-gstore: ⊦ n ∈ nx ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore; (forward) from specification apersistence-base% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ unbuffered ≠ readonly; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%⊦ ¬ pstate.journal? → (pstate.index? ↔ pstate ≠ unbuffered ∧ pstate ≠ readonly); (ss)