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Theorem abs-nodes-valid-node

⊦ is-encoded(nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)) ∧ 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf ∧ range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE) → ( abs-nodes(buf, n, x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( boolvar0 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, x, lax, weak) ∨ # buf0 = x.head.flashsize ∧ x ≠ [] ∧ lax ≠ [] ∧ lax.head = @(n, # buf0) ∧ ¬ boolvar0 ∧ abs-node(buf0, x.head) ∧ abs-nodes(buf1, n + # buf0, x.tail, lax.tail, weak))))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 11
Proof steps: 29
Used lemmas: ls-abs-node-buf-size, abs-nodes-first-adr-explicit, abs-nodes-rec, abs-nodes-headerspace, abs-nodes-mkbuf0-empty-h, abs-nodes-base, abs-nodes-elems-empty-adr-empty-h, abs-nodes-padding-prefix,
Used spec theorems:
Used simplifier rules:
- encoding-node-base/node-flash-size
- nat-basic/z-01
- nat/lez-01
- array/buffer/Size-mkarray
- nat/ge
- align/is-aligned-same
- align/is-aligned-add
- encoding-fixed-size-nonempty/encoding-node-header/is-encoded-not-garbage-nonempty
- node-header/sel
- nat/let
- nat/le-add
- array-splice/buffer/append-zero-right
- list/c-07
- list/c-08
- list/c
- laddress/elim
- list-data/laddress-list/elim-list-c
- list/laddress-list/a
- list/laddress-list/e-01
- list/laddress-list/c
- align/is-aligned-mod
- abs-node/buf-size-zero
- list/e-01
- list/a
- nat-mult/two-02
- array-splice/buffer/append-len
- node-header-size/validtrailer-size
- nat-mult/numeral-19
- nat-mult/one
- array-splice/buffer/subarray-append-left
- encoding-fixed-size-nonempty/encoding-node-header/is-encoded-unique
- node-header/inj
- array-copy/buffer/subarray-elim
- nat-mult/two-zero-01
- align/alignup-same
- nat-mult/numeral-20
- laddress/inj
- nat-basic/f
- nat-basic/lf-02
- node-header-size/nodeheader-notzero
- nat-mult/ls-08
- abs-node/abs-node-no-abs-padding
- abs-node/abs-node-abs-node
- array-splice/buffer/append-eq-left
- array-copy/buffer/size-subarray
- abs-node/lfw-is-encoded-nodeheader-size
- abs-node/abs-padding-eq
- nat/lep
- nat/lep-02
- nat-mult/mult-c
- nat-mult/mult-a
- abs-node/abs-padding-alignup
- abs-node/abs-padding-size
- array-splice/buffer/append-a
- array-splice/buffer/subarray-elim-right
- abs-node/abs-padding-nospace
- nat/le-def
- nat-basic/add-base
- nat-basic/a
- nat-basic/c