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Proof step 57 from proof validref-putrkvs (previous step)

rk = r0 -- sk, validref(str, r, ty, st), validval(str, rk, val, st), validvals(str, rkvs0, st), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ validref(str, r, ty, st[rk, val]), validref(str, r, ty, st[rk, val][rkvs0]), ( is_fskey(sk) → (is_referencevalue(val) → validref(str, val .refval, sk .fs .type, st) ∧ is_reftype(sk .fs .type)) ∧ (¬ is_referencevalue(val) → okval(val, sk .fs .type) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length)) ∧ ( is_indexkey(sk) → ( is_referencevalue(val) → validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[r0 -- _type] .type .type)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
validref(str, r, ty, st), validval(str, r0 -- sk, val, st), validvals(str, rkvs0, st), ∀ 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]), ( is_fskey(sk) → (is_referencevalue(val) → validref(str, val .refval, sk .fs .type, st) ∧ is_reftype(sk .fs .type)) ∧ (¬ is_referencevalue(val) → okval(val, sk .fs .type) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length)) ∧ ( is_indexkey(sk) → ( is_referencevalue(val) → validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[r0 -- _type] .type .type)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]