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Proof step 12 from proof validrefs-applast-array (previous step)

validrefs(str, refs + r ', ty, st), is_array(str, r, st), i < st[r -- _length] .intval, st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type, is_valid_ref(str, st[r -- i '] .refval, st), type∃(str, st[st[r -- i '] .refval -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ validrefs(str, refs + r ' + st[r -- i '] .refval ', ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
st[r -- i '] = refval(r0) ∧ is_referencevalue(st[r -- i ']), validrefs(str, refs + r ', ty, st), is_array(str, r, st), i < st[r -- _length] .intval, st[r0 -- _type] .type ≤ st[r -- _type] .type .type, is_valid_ref(str, r0, st), type∃(str, st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ validrefs(str, refs + r ' + r0 ', ty, st)

Rule argument

[speclemmaarg: is_referencevalue(val) ,r = val .refval ↔ val = refval(r) ,[val, r] → [st[r -- i '], r0] ,T ,javavalue , ,elim-refval ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPSEQ : ⊦ ¬ is_valid_ref(str, jvmref, st)], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r -- i '], r0)]]