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Proof step 18 from proof validrefs-putbar (previous step)

jvmref = (putByteArray(bytes, r1, i, st)[r1 -- i0 ']) .refval, 0 < st[r1 -- _length] .intval, 0 ≤ i0, is_referencevalue(putByteArray(bytes, r1, i, st)[r1 -- i0 ']), i0 < st[r1 -- _length] .intval, mkarraytype(byte_type) ≤ ty, is_array(`docs2store', r1, putByteArray(bytes, r1, i, st)), okbytearray(r1, st), ∀ r1, st, ty, bytes, i. okbytearray(r1, st) ∧ validrefs(`docs2store', jvmref ', ty, putByteArray(bytes, r1, i, st)) → validrefs(`docs2store', jvmref ', ty, st) ⊦ r1 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r1 -- i1 ']) ∧ jvmref = st[r1 -- i1 '] .refval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
(putByteArray(bytes, r1, i, st)[r1 -- i0 ']) = refval(r), jvmref = r, 0 < st[r1 -- _length] .intval, 0 ≤ i0, is_referencevalue(putByteArray(bytes, r1, i, st)[r1 -- i0 ']), i0 < st[r1 -- _length] .intval, mkarraytype(byte_type) ≤ ty, is_array(`docs2store', r1, putByteArray(bytes, r1, i, st)), okbytearray(r1, st), ∀ r1, st, ty, bytes, i. okbytearray(r1, st) ∧ validrefs(`docs2store', jvmref ', ty, putByteArray(bytes, r1, i, st)) → validrefs(`docs2store', jvmref ', ty, st) ⊦ r1 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r1 -- i1 ']) ∧ jvmref = st[r1 -- i1 '] .refval

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [putByteArray(bytes, r1, i, st)[r1 -- i0 '], r] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (putByteArray(bytes, r1, i, st)[r1 -- i0 '], r)]]