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Proof step 52 from proof validref-putrkvs (previous step)

sk .fs = mkfs(class, ty0, fieldvar), validvals(str, rkvs0, st), validref(str, r, ty, st), ¬ is_fskey(sk) → validval(str, val, st[r0 -- _type] .type .type, st), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]), ¬ is_indexkey(sk) → validval(str, val, ty0, st) ∧ ty0 ≠ 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)), validref(str, r, ty, st[r0 -- sk, val][rkvs0]), validref(str, r, ty, st[r0 -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
sk .fs = mkfs(class, ty0, fieldvar), is_indexkey(sk), validvals(str, rkvs0, st), validref(str, r, ty, st), validval(str, val, st[r0 -- _type] .type .type, 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][rkvs0]), validref(str, r, ty, st[r0 -- sk, val]), ( 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 : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])]]