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Theorem inv-add-gnds

lpt-free-unref(lpt), lpt-free-unref(lpt0), freelist-cons(lpt, freelist), log = log0, bin-heap-inv(gch, lpt), keyset(gch) = gc-heap(lpt, log), bufs-log-only(bleb, log, lpt), # lpt = # avol, ¬ dups(log), log-group-block(log, lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log), m = LEB_SIZE, awbuf-inv(avol, bleb), # lpt0 = # avol, ¬ isbuf → bleb.isbuf? ∧ bleb.leb < # lpt ∧ lpt[bleb.leb].flags = LP_GROUP_NODES ∧ bleb.leb ∈ log ∧ avol[bleb.leb].mapped? ∧ (gndx ≠ [] ∧ lpt[bleb.leb].size + gndx.flashsize ≤ LEB_SIZE → lpt[bleb.leb].size = # avol[bleb.leb].data) ⊦ ⟪persistence_add_gnds#(gndx, log, m, adr, m0, log0, lpt0, ns, bleb; ax, lpt, avol, isbuf; err)⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ bufs-log-only(bleb, log, lpt) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ buf-ro-rw-mode(isbuf, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol)

Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state: persistence-refine,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 82
Used lemmas: prepost-encode-group-nodes, elim-mapped, elim-lp-upd-size, add-gnds,
Used spec theorems:
- awbuf-asm/inv-write-buf
- debug/debug
Used simplifier rules:
- lprops/elim
- persistence-base/buf-ro-rw-mode-switch
- bufleb/elim-is-buf-ant
- lprops/inj
- nat/le-def
- abs-list/encoding-group-node/abs-nodes-elems-adr-length-h
- bufleb/disj
- error-class/esuccess
- persistence-base/buf-ro-rw-mode-write
- array-splice/buffer/append-len
- array-splice/buffer/append-a
- nat-basic/eq-01
- nat/lels-03
- abs-list/encoding-group-node/flashsize-eq-0
- aleb/inj
- awbuf-inv/inv-buf-in-vol
- nat-basic/f
- nat-basic/lf-01
- nat-basic/add-base
- array/avolume/Size-put
- eraseblock/page-size
- align/is-aligned-add
- nat-basic/a
- nat-basic/c
- array-copy/buffer/subarray-elim
- nat/lels
- nat/fle-01
- nat/fle
- oelem/nat-set/irreflexivity
- persistence-base/lpt-free-unref-write
- elem-index/gc-heap-base/sel-01-M03
- elem-index/gc-heap-base/sel-01-M01
- elem-index/gc-heap-base/sel-02
- persistence-base/bufs-log-only-write-lpt-same-flags
- array/lp-array/Size-put
- persistence-base/buf-ro-rw-mode-leb-size
- persistence-base/lpt-leb-size-write
- nat/ls-le-simp
- elem-index/gc-heap-base/sel-01-M02
- nat/ler
- lprops/disj-01
- persistence-base/freelist-cons-write-lpt-other
- persistence-base/bin-heap-inv-write-other-fields
- persistence-base/gc-heap-write-nochange
- persistence-base/log-group-block-write-at
- persistence-base/lpt-ram-flash-write-log-buf
- aleb/sel
- aleb/test-02
- bufleb/sel
- bufleb/test-02
- error-class/not-esuccess