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Proof step 58 from proof validval-put-any (previous step)

validval(str, rk, val, st), is_reftype(ty), validref(str, r0, ty, st) ⊦ r -- _type = rk, mkfs(class, ty, fieldvar) ' = _length, ty = void_type, validref(str, r0, ty, st[rk, val]), ( is_fskey(rk .key) → (is_referencevalue(val) → validref(str, val .refval, rk .key .fs .type, st) ∧ is_reftype(rk .key .fs .type)) ∧ (¬ is_referencevalue(val) → okval(val, rk .key .fs .type) ∧ rk .key .fs .type ≠ void_type ∧ rk .key ≠ _length)) ∧ ( is_indexkey(rk .key) → ( is_referencevalue(val) → validref(str, val .refval, st[rk .ref -- _type] .type .type, st) ∧ rk .ref ≠ jvmref ∧ is_arraytype(st[rk .ref -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[rk .ref -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[rk .ref -- _type] .type .type)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
rk = r1 -- sk, validval(str, rk, val, st), is_reftype(ty), validref(str, r0, ty, st) ⊦ r -- _type = rk, mkfs(class, ty, fieldvar) ' = _length, ty = void_type, validref(str, r0, ty, st[rk, val]), ( 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[r1 -- _type] .type .type, st) ∧ r1 ≠ jvmref ∧ is_arraytype(st[r1 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r1 -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[r1 -- _type] .type .type)))

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [rk, r1, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (rk, r1, sk)]]