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Theorem exvalidrefs-nodups

¬ junkref(str, r, st), ¬ cyclic(str, r, st), is_obj(str, r, st), r ≠ jvmref, ∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st[r -- _type] .type ≤ fs .type ⊦ ∃ refs. validrefs(str, refs, st[r -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: The exists fs, class is necessary because we may have an object that has no reference field. In this case validrefs cannot end with null!
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 53
Proof steps: 134
Used lemmas: validrefs-null-01, validrefs-delete-01, validrefs-del-junkrefs, validrefs-one, validrefs-class, cyclic-def-simple,
Used spec theorems:
Used simplifier rules:
- okfuns/good-field-field-01
- valuefuns/okval-class
- store/javastore/In-store
- javavalue/test-92
- javavalue/elim-10
- storefuns/instore-01
- list-last/references/last-def
- javatype/sel-02
- typefuns/transitivity-01
- classnamefuns/le-reflexive
- list-last/references/l-05
- list-dup/references/c-02
- list/references/app-02-ant
- list-last/references/l-02
- list/references/app
- list-last/references/l
- addfuns/is_valid_ref
- okfuns/is_array-typele
- addfuns/isarray-isobj-01
- addfuns/instfields-Object
- list/storekeys/in-empty
- list-dup/references/rec
- list-dup/references/e-01
- junkrefs/junkrefs-junkref
- addfuns/instfields-subclass
- classnamefuns/le-transitive
- typefuns/class-le
- javatype/test-10
- typefuns/subclass
- javatype/elim-02
- list/references/in-append
- list-dup/references/f
- junkrefs/junkrefs-notin-03
- list/references/in-13
- list/references/in-01
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c
- storefuns/look-del
- addfuns/is_obj-del
- addfuns/is_obj-notin
- set-union/references/size-del-leq
- nat/lels
- storefunsx/refs-del
- javavalue/sel-09
- addfuns/instfields-subclass-in
- list/references/first
- list/references/e
- typefuns/ref
- list/references/c-08
- list/references/a
- list/references/in-17
- list-dup/references/c
- list-dup/references/dups-cons
- javavalue/test-19
- javavalue/elim-13
- addfuns/is_obj-classtype
- fieldspec/sel-03
- addfuns/is_valid_ref-isobj
- fieldspec/elim
- typefuns/transitivity