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Theorem disjoint-def-fits

⊦ validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st) → ( disjoint(str, refs, st) ↔ ¬ (∃ r1, sks1, r2, sks2. r1 ∈ refs ∧ r2 ∈ refs ∧ r1 ≠ r2 ∧ fits(r1, sks1, st) ∧ fits(r2, sks2, st) ∧ st[r1 -- sks1] = st[r2 -- sks2] ∧ st[r1 -- sks1] .refval ≠ jvmref))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: addarray-disjoint-nosharing, addarray-disjoint-nosharing-01, hasSharing-addobj-same, hasSharing-put-index-refval,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 14
Proof steps: 36
Used lemmas: ex-validrefs-fits, ex-fits-validrefs, disjoint-def,
Used spec theorems:
- junkrefs/validreflist-def
- valuesfuns/javavalues-in
Used simplifier rules:
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c
- list/references/app-02-ant
- list/references/e
- list/references/a
- list/references/c-08
- junkrefs/validref-junkref
- javavalue/sel-09
- javavalue/test-19
- valuefuns/refval-xtra
- javavalue/elim-refval