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Proof step 27 from proof pathexplus-pathex (previous step)

0 < st[(r ' + refs) .last -- _length] .intval, 0 ≤ i, validrefs(str, st[(r ' + refs) .last -- i '] .refval ', st[(r ' + refs) .last -- _type] .type .type, st), is_referencevalue(st[(r ' + refs) .last -- i ']), i < st[(r ' + refs) .last -- _length] .intval, is_arraytype(st[(r ' + refs) .last -- _type] .type), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + st[(r ' + refs) .last -- i '] .refval ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st), is_array(str, (r ' + refs) .last, st) ⊦ r = st[(r ' + refs) .last -- i '] .refval, r = jvmref, (r ' + refs) .last = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i0 ∧ is_referencevalue(st[(r ' + refs) .last -- i0 ']) ∧ st[(r ' + refs) .last -- i0 '] .refval = st[(r ' + refs) .last -- i '] .refval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
st[(r ' + refs) .last -- _type] .type = mkarraytype(ty), 0 < st[(r ' + refs) .last -- _length] .intval, 0 ≤ i, validrefs(str, st[(r ' + refs) .last -- i '] .refval ', ty, st), is_referencevalue(st[(r ' + refs) .last -- i ']), i < st[(r ' + refs) .last -- _length] .intval, is_arraytype(st[(r ' + refs) .last -- _type] .type), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + st[(r ' + refs) .last -- i '] .refval ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st), is_array(str, (r ' + refs) .last, st) ⊦ r = st[(r ' + refs) .last -- i '] .refval, r = jvmref, (r ' + refs) .last = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i0 ∧ is_referencevalue(st[(r ' + refs) .last -- i0 ']) ∧ st[(r ' + refs) .last -- i0 '] .refval = st[(r ' + refs) .last -- i '] .refval

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[(r ' + refs) .last -- _type] .type, ty] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[(r ' + refs) .last -- _type] .type, ty)]]