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Theorem validrefs-subset-01

⊦ validrefs(str, refs, ty, st) ∧ st ⊆ st0 ∧ ¬ junkref(str, r, st) ∧ refs ≠ [] ∧ refs .first = r → validrefs(str, refs, ty, st0)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: cyclic-subset-01, pathex-subset, validrefs-subset-equiv,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 23
Proof steps: 58
Used lemmas: validrefs-null-01, validrefs-array, validrefs-null-02, validrefs-class, validrefs-is-junk, validrefs-null,
Used spec theorems:
Used simplifier rules:
- int-abs/lels-03
- okfuns/is_array-lenfield
- int-abs/lels-04
- int-abs/forward-le-01
- int-abs/forward-le-05
- int-abs/lels
- int-abs/lels-01
- okfuns/is_array-type-02
- okfuns/is_array-subset
- addfuns/is_valid_ref-isarray
- javavalue/sel-09
- javavalue/disj-19
- fieldspec/sel-03
- storefuns/instore-01
- store/javastore/notmemlookup
- storefunsx/lookup-xtra
- javavalue/test-19
- javavalue/elim-13
- list-data/references/elim-list-c
- addfuns/is_obj-type
- addfuns/is_obj-subset
- fieldspec/elim
- addfuns/is_valid_ref-isobj
- list/references/app
- list/references/c-08
- list/references/a
- list/references/e-01
- list/references/c