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Proof step 122 from proof pathex-put-pathex-array-refval (previous step)

path∃(str, r, r1, st[r0 -- i ', val]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, is_referencevalue(val), validref(str, val .refval, st[r0 -- _type] .type .type, st), is_arraytype(st[r0 -- _type] .type), 0 < st[r0 -- _length] .intval, 0 ≤ i, val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type) ⊦ r0 = jvmref, path∃(str, r, r1, st), path∃(str, val .refval, r1, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 121:
val = refval(r2), path∃(str, r, r1, st[r0 -- i ', val]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, is_referencevalue(val), validref(str, r2, st[r0 -- _type] .type .type, st), is_arraytype(st[r0 -- _type] .type), 0 < st[r0 -- _length] .intval, 0 ≤ i, r2 = jvmref → is_reftype(st[r0 -- _type] .type .type) ⊦ r0 = jvmref, path∃(str, r, r1, st), path∃(str, r2, r1, st)

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] → [val, 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 : (val, r2)]]