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Proof step 122 from proof validrefs-put-notin-03 (previous step)

refs0 + r ' = st[r1 -- i '] .refval ' + refs2, is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(refs1) ∩ list2set(refs0) = ∅, 0 < st[r1 -- _length] .intval, 0 ≤ i, i < st[r1 -- _length] .intval, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), is_valid_ref(r1, st), validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st), is_referencevalue(st[r1 -- i ']), ∀ str0, r2, st0, sk0, val0, refs, r3, ty0. (is_valid_ref(str0, r2, st0) ↔ is_valid_ref(str0, r2, st0[r2 -- sk0, val0])) ∧ list2set(refs0) ∩ list2set(refs) = ∅ → val0 .refval = r3 ∨ r3 = st0[r2 -- sk0] .refval ∨ sk0 = _type ∨ sk0 = _length ∨ (validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0)) ∨ r2 = r3 ∨ r3 ∈ refs0 ∨ r2 ∈ refs ∨ r2 ∈ refs0 ∨ dups(refs) ∨ r3 ∈ refs ⊦ r0 = r1, r = r1, r1 = jvmref, r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, dups(refs1), r0 ∈ refs1, r1 ∈ refs1, dups(refs0), r1 ∈ refs0, r0 ∈ refs0, r ∈ refs1, r ∈ refs0, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ st[r1 -- i '] .refval = st[r1 -- i0 '] .refval ∧ validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st[r -- sk, val]), r ≠ st[r1 -- i '] .refval ∧ ¬ r ∈ refs2, ¬ st[r1 -- i '] .refval ∈ refs0 ∧ st[r1 -- i '] .refval ≠ r

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 121:
st[r1 -- i '] = refval(r4), refs0 + r ' = r4 ' + refs2, is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(refs1) ∩ list2set(refs0) = ∅, 0 < st[r1 -- _length] .intval, 0 ≤ i, i < st[r1 -- _length] .intval, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), is_valid_ref(r1, st), validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st), is_referencevalue(st[r1 -- i ']), ∀ str0, r2, st0, sk0, val0, refs, r3, ty0. (is_valid_ref(str0, r2, st0) ↔ is_valid_ref(str0, r2, st0[r2 -- sk0, val0])) ∧ list2set(refs0) ∩ list2set(refs) = ∅ → val0 .refval = r3 ∨ r3 = st0[r2 -- sk0] .refval ∨ sk0 = _type ∨ sk0 = _length ∨ (validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0)) ∨ r2 = r3 ∨ r3 ∈ refs0 ∨ r2 ∈ refs ∨ r2 ∈ refs0 ∨ dups(refs) ∨ r3 ∈ refs ⊦ r0 = r1, r = r1, r1 = jvmref, r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, dups(refs1), r0 ∈ refs1, r1 ∈ refs1, dups(refs0), r1 ∈ refs0, r0 ∈ refs0, r ∈ refs1, r ∈ refs0, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r4 = st[r1 -- i0 '] .refval ∧ validrefs(str, refs0 + r ' + r0 ' + refs1, st[r1 -- _type] .type .type, st[r -- sk, val]), r ≠ r4 ∧ ¬ r ∈ refs2, ¬ r4 ∈ refs0 ∧ r4 ≠ r

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r1 -- i '], r4] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r1 -- i '], r4)]]