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Proof step 51 from proof validrefs-put-array-badindex (previous step)

0 < st[r0 -- _length] .intval, 0 ≤ i0, i0 < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- i ', val]), i < 0, is_array(str, r0, st), validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st), is_referencevalue(st[r0 -- i0 ']), i < st[r0 -- _length] .intval, ∀ i, str0, ty0, st0, r1, val0. ¬ 0 ≤ i → (validrefs(str0, st[r0 -- i0 '] .refval ' + refs, ty0, st0[r1 -- i ', val0]) ↔ validrefs(str0, st[r0 -- i0 '] .refval ' + refs, ty0, st0)) ⊦ r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i ', val][r0 -- i1 ']) ∧ st[r0 -- i0 '] .refval = (st[r -- i ', val][r0 -- i1 ']) .refval ∧ validrefs(str, (st[r -- i ', val][r0 -- i1 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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[r0 -- i0 '], r2] 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[r0 -- i0 '], r2)]]