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Proof step 61 from proof validrefs-put-array-badindex (previous step)

i < 0, is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st[r -- i ', val]), ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 60:
i < 0, is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st[r -- i ', val]), ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

Rule argument

[x0lemmaarg: spec-name: addfuns instance-name: lemma-name: is-valid-ref-stronger-def antecedent: succedent: is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) substlist: [st, r, str] → [st, r0, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, str)]]