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Theorem validrefs-subset-equiv

⊦ validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 → (validrefs(str, r ' + refs, ty, st0) ↔ validrefs(str, r ' + refs, ty, st))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 36
Proof steps: 77
Used lemmas: validrefs-subset-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null-02,
Used spec theorems:
Used simplifier rules:
- list/references/c-08
- list/references/app-02-ant
- list/references/e
- junkrefs/validref-junkref
- okfuns/is_array-type-02
- int-abs/lels-03
- okfuns/is_array-lenfield
- int-abs/forward-lels
- javavalue/test-02
- int-abs/lels-04
- int-abs/forward-le-01
- int-abs/forward-le-05
- int-abs/lels
- int-abs/lels-01
- addfuns/is_valid_ref-isarray
- okfuns/is_array-subset
- addfuns/is_obj-isarray
- addfuns/is_valid_ref-01
- junkrefs/junkref-null
- list/references/len
- list/references/len-02
- nat-basic2/s
- nat-basic1/ref-1
- nat-basic2/a
- nat-basic2/c
- javavalue/sel-09
- addfuns/is_obj-notin-01
- store/javastore/notmemlookup
- storefunsx/lookup-xtra
- addfuns/is_obj-type
- fieldspec/sel-03
- javavalue/test-19
- javavalue/elim-13
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c
- addfuns/is_valid_ref-isobj
- addfuns/is_obj-subset
- okfuns/is_array-classtype
- storefuns/instore-01
- addfuns/isarray-isobj-01
- addfuns/is_valid_ref
- addfuns/is_valid_ref-notin-01
- fieldspec/elim
- list/references/a