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Proof step 124 from proof pathex-put-pathex-array-refval (previous step)

path∃(str, r, r1, st[r0 -- sk, val]), path∃(str, r, r0, st), is_indexkey(sk), sk .index < st[r0 -- _length] .intval, is_referencevalue(val), validref(str, val .refval, st[r0 -- _type] .type .type, st), is_arraytype(st[r0 -- _type] .type), 0 ≤ sk .index, 0 < st[r0 -- _length] .intval, 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 123:
sk = i ', path∃(str, r, r1, st[r0 -- sk, val]), path∃(str, r, r0, st), is_indexkey(sk), 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 ≤ i, 0 < st[r0 -- _length] .intval, val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type) ⊦ r0 = jvmref, path∃(str, r, r1, st), path∃(str, val .refval, r1, st)

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: elim-04 antecedent: succedent: is_indexkey(sk) → (i = sk .index ↔ sk = i ') substlist: [sk, i] → [sk, i] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_indexkey(sk) → (i = sk .index ↔ sk = i ')])], [EXTRATERMS : (sk, i)]]