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Proof step 20 from proof inv-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, isbuf ↔ false, lpt1[n] = mklp(m4, m1, LP_GROUP_NODES, m2), avol[n] = mapped(buf), bleb0 = buffered(n), keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, n < # avol, awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), 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), n ∈ log0, m1 + gndx.flashsize ≤ LEB_SIZE → m1 = # buf ⊦ ⟪persistence_encode_group_nodes#(gndx, bleb0.leb, lpt1[bleb0.leb].size; ; buf, ax, err); isbuf1 := false; bleb1 := buffered(n); if err = ESUCCESS then if ¬ lpt1[bleb0.leb].size + # buf ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr, m, log0, avol, lpt0, ns, bleb1; ; isbuf1); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr, m, log0, lpt0, ns, bleb1; avol, isbuf1; err); if err = ESUCCESS then lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, lpt1[bleb0.leb].size + # buf, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + bleb0.leb.toString + " failed"); lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, LEB_SIZE, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx)}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr, m, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol), gndx = [], dups(log0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
# lpt0 = # avol, # lpt1 = # avol, isbuf ↔ false, avol[n] = mapped(buf), lpt1[n] = mklp(m4, m1, LP_GROUP_NODES, m2), lpt1[bleb0.leb] = mklp(m0, m3, lpf, m5), bleb0 = buffered(n), keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, n < # avol, awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), 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), n ∈ log0, m1 + gndx.flashsize ≤ LEB_SIZE → m1 = # buf ⊦ ⟪persistence_encode_group_nodes#(gndx, bleb0.leb, m3; ; buf, ax, err); isbuf1 := false; bleb1 := buffered(n); if err = ESUCCESS then if ¬ m3 + # buf ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr, m, log0, avol, lpt0, ns, bleb1; ; isbuf1); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr, m, log0, lpt0, ns, bleb1; avol, isbuf1; err); if err = ESUCCESS then lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, lpt1[bleb0.leb].size + # buf, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + bleb0.leb.toString + " failed"); lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, LEB_SIZE, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx)}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr, m, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol), gndx = [], dups(log0)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt1[bleb0.leb], m3, m4, lpf, m5]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt1[bleb0.leb], m3, m4, lpf, m5