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Proof step 73 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, gstore[log1.last] = groupblock(gndx, lax, m0), lpt1[log1.last] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[log1.last] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, gndx0 ≠ [], log1 ≠ [], 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(groupblock(gndx, lax, m0)), 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), m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # buf ⊦ [persistence_encode_group_nodes#(gndx0, buffered(log1.last).leb, m1; ; buf, ax, err); isbuf2 := false; bleb1 := buffered(log1.last); if err = ESUCCESS then if ¬ m1 + # buf ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf2); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr0, m, log1, lpt0, ns0, bleb1; avol, isbuf2; err); if err = ESUCCESS then lpt1[buffered(log1.last).leb] := mklp (lpt1[buffered(log1.last).leb].ref-size, lpt1[buffered(log1.last).leb].size + # buf, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(log1.last).leb.toString + " failed"); lpt1[buffered(log1.last).leb] := mklp (lpt1[buffered(log1.last).leb].ref-size, LEB_SIZE, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx)}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb1, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol → ⟨pstate := journal(log1.last); apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum)) ∧ ax = ax0 ∧ err = err0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list, inst: nat-list-set name: lastdiv-rew seq: ⊦ nx = [] ↔ ¬(∃ nx0, n. nx = nx0 + n ') subst: [nx] → [log1] flags: <all paths>

Additional information

Used terms: log1