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Theorem prepost-write-orphans

n < # avol, ebm-vol-inv(avol), avol0 = avol, orphans0 = orphans ⊦ ⟪persistence_io_write_orphans#(n, EB_PAGE_SIZE, LEB_SIZE; orphans, avol; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ebm-vol-inv(avol) ∧ id○(avol, avol0, n) ∧ (err = ESUCCESS → avol[n].mapped? ∧ is-encoded-pad(orphans0, # orphans0, avol[n].data)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: inv-commit,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 65
Used lemmas: prepost-encode-orphans, write-orphans,
Used spec theorems:
Used simplifier rules:
- nat-basic/f
- nat/ler
- array-copy/buffer/subarray-elim
- encoding-orphans/is-encoded-pad-unique
- set-basic/nat-set/size-zero
- nat/lez
- set-basic/nat-set/size-zero-01
- set-basic/nat-set/Size-empty
- encoding-orphans/is-encoded-pad-empbuf
- error-class/esuccess
- array-splice/buffer/append-left-size0
- nat-basic/z-01
- array-splice/buffer/append-len
- nat-mult/zero-06
- encoding-fixed-size/encoding-nat/encoding-requires-space
- nat-mult/mult-a
- nat-mult/mult-c
- array/avolume/Put-same
- aleb/sel
- array/buffer/Size-mkarray
- nat-basic/add-base
- nat-basic/a
- nat-basic/c
- nat/lels-03
- array-splice/buffer/append-zero-left
- array-splice/buffer/mkemparray0-append-left
- array-splice/buffer/append-a
- nat/lels
- nat/ls-le-simp
- array/avolume/cputput
- array/avolume/Size-put
- aleb/test-02
- encoding-elem-alignment/encoding-superblock/alignment-not-zero
- align/is-aligned-zero
- nat-basic/zero
- array-copy/avolume/idexcept-write-at0
- error-class/not-esuccess
- array-copy/avolume/idexcept-refl