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Theorem map-path

⊦ reachset(r0, H) ⊆ dom map ∧ inj(map) ∧ closed(H) → (path(x, r0, r1, H) ↔ path(x, map[r0], map[r1], apply(H, map)) ∧ r0 ∈ map ∧ r1 ∈ map)

Type: A user defined theorem
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: 19
Proof steps: 42
Used lemmas: reachable-one, reachset-succ, closed-succ, at-apply-succ, in-apply-succ, at-apply, path-rec, reachable-eq, reachset, inj-eq, in-apply, path-emp, path-first-in,
Used spec theorems:
- set-union/refset/subdef
Used simplifier rules:
- store+set/ref-map-store+set-r/Dom
- list/a
- list/c
- node/elim
- node/sel-01
- node/inj
- store/ref-map/notmemlookup
- set-basic/refset/sub-ntrans-01