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Proof step 45 from proof validref-putrkvs (previous step)

val = refval(r1), sk .fs = mkfs(class, ty0, fieldvar), validval(str, val, st[r0 -- _type] .type .type, st), validref(str, r, ty, st), validvals(str, rkvs0, st), is_indexkey(sk), is_referencevalue(val), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ validref(str, r, ty, st[r0 -- sk, val]), validref(str, r, ty, st[r0 -- sk, val][rkvs0]), validref(str, r1, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (r1 = jvmref → is_reftype(st[r0 -- _type] .type .type))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
sk .fs = mkfs(class, ty0, fieldvar), validval(str, refval(r1), st[r0 -- _type] .type .type, st), validref(str, r, ty, st), validvals(str, rkvs0, st), is_indexkey(sk), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ validref(str, r, ty, st[r0 -- sk, refval(r1)]), validref(str, r, ty, st[r0 -- sk, refval(r1)][rkvs0]), validref(str, r1, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (r1 = jvmref → is_reftype(st[r0 -- _type] .type .type))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]