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Theorem lst-in-hp

⊦ (o[lst(r)] * R)[rs, cf, af] ∧ r ≠ null → (¬ r ∈ rs ↔ false)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 17
Used lemmas: ls-rec, ls-base, ex-lst-shift, lst-def,
Used spec theorems:
- heap-fun/cell-heap-aux-heap-aux/sep
- heap-fun/cell-heap-aux-heap-aux/apply
- embed-aux/cell-heap-aux/lift-aux
- heap-sep/cell-heap-aux/sep
- maplet/cell-heap-aux/maplet
- heap/cell-heap-aux/ext
Used simplifier rules:
- heap/cell-heap-aux/at-uni
- heap-fun/cell-heap-aux/at-mk
- heap/cell-heap-aux/in-write-strong
- heap/cell-heap-aux/in-emp
- heap/cell-heap-aux/in-alloc
- heap/cell-heap-aux/in-uni
- set-union/refset/int-c
- set-union/refset/int-a
- heap-fun/cell-heap-aux/in-mk
- maplet/cell-heap-aux/ex1
- list/a
- list/c
- heap-sep/cell-heap-aux/false-rev
- heap-sep/cell-heap-aux/false-and
- heap-sep/cell-heap-aux/and-ass
- heap-sep/cell-heap-aux/and-com
- heap-sep/cell-heap-aux/falseH
- set-union/refset/unc
- set-union/refset/una
- set-union/refset/Union