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Proof step 4 from proof validref-nopathex-put (previous step)

⊦ is_valid_ref(str, r0, st) ∧ sk ≠ _type ∧ ¬ path∃(str, r, r0, st) → ( r = jvmref ∨ (st[r0 -- sk, val][r -- _type]) .type ≤ ty ∧ ¬ junkref(str, r, st[r0 -- sk, val]) ↔ r = jvmref ∨ st[r -- _type] .type ≤ ty ∧ ¬ junkref(str, r, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: junkref-put-nopathex-equiv-01 antecedent: succedent: ¬ path∃(str, r, r0, st) ∧ sk ≠ _type ∧ is_valid_ref(str, r0, st) → ( junkref(str, r, st[r0 -- sk, val]) ↔ junkref(str, r, st)) substlist: [val, sk, r0, st, r, str] → [val, sk, r0, st, r, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javastore, , at-other-16, ⊦ sk ≠ sk0 → (st[r -- sk, val] [r0 -- sk0 ] ) = st[r0 -- sk0]])], [EXTRATERMS : (val, sk, r0, st, r, str)]]