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Theorem inv-set-gblock-refsize

lpt-free-unref(lpt), 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-ram-flash(lpt, lpt0, log), m < # lpt, lpt[m].flags = LP_GROUP_NODES ⊦ ⟪persistence_set_gblock_refsize#(m, n, log; lpt, gch)⟫ ( 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))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 22
Used lemmas: set-gblock-refsize,
Used spec theorems:
- persistence-base/gc-heap-in
- bin-min-heap-prepost/gc-heap-rename-gc-heap-base/prepost-update
- persistence-base/log-group-block-id-idx
- persistence-base/lpt-ram-flash-id-idx
- persistence-base/lpt-ram-flash-write-same
- index-array/gc-heap-base/id-idx
Used simplifier rules:
- lprops/elim
- nat/fle-01
- nat/fle
- oelem/nat-set/irreflexivity
- set-basic/gc-heap-rename-gc-heap-base-keyindex-set/size-zero-01
- set-basic/gc-heap-rename-gc-heap-base-keyindex-set/ne-01
- elem-index/gc-heap-base/sel-01-M01
- persistence-base/lpt-leb-size-id-idx
- persistence-base/buf-ro-rw-mode-id-idx
- persistence-base/bufs-log-only-id-idx
- persistence-base/id-idx-gcheap
- persistence-base/id-idx-freelist-cons
- persistence-base/id-idx-lpt-free-unref
- persistence-base/gc-heap-update
- persistence-base/lpt-free-unref-write
- lprops/updsel-03
- lprops/updsel-09
- elem-index/gc-heap-base/sel-01-M03
- lprops/upd-04
- persistence-base/bufs-log-only-write-lpt-same-flags
- array/lp-array/Size-put
- persistence-base/lpt-leb-size-write
- nat/ls-le-simp
- lprops/updsel-06
- nat-basic/lf-01
- lprops/disj-01
- persistence-base/freelist-cons-write-lpt-other
- nat/lels
- persistence-base/bin-heap-inv-write-other-fields
- persistence-base/gc-heap-update-log
- persistence-base/log-group-block-write-at
- persistence-base/buf-ro-rw-mode-write-other-fields
- elem-index/gc-heap-base/sel-01-M02
- nat/le-def
- persistence-base/lpt-leb-size-at
- persistence-base/lpt-ram-flash-write-same
- nat-basic/f