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Proof step 120 from proof pathex-put-pathex-array-refval (previous step)

path∃(str, r, r1, st[r0 -- i ', refval(r2)]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 119:
st[r0 -- _type] .type = mkarraytype(ty), path∃(str, r, r1, st[r0 -- i ', refval(r2)]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), is_arraytype(st[r0 -- _type] .type), 0 < st[r0 -- _length] .intval, 0 ≤ i, r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, path∃(str, r, r1, st), path∃(str, r2, r1, st)

Rule argument

[x0lemmaarg: spec-name: javatype instance-name: lemma-name: elim-01 antecedent: succedent: is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) substlist: [ty, ty0] → [st[r0 -- _type] .type, ty] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r0 -- _type] .type, ty)]]