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Proof step 53 from proof validval-put-any (previous step)

sk .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, ty, st), is_reftype(ty), validval(str, r1 -- sk, val, st), is_indexkey(sk), r ≠ r1 ∨ _type ≠ sk ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- sk, val]), ( 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ validval(str, r -- sk, val, st) ↔ (is_fskey(sk) → validval(str, val, sk .fs .type, st) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, st[r -- _type] .type .type, st))
Proof step 52:
sk .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, ty, st), is_reftype(ty), (is_fskey(sk) → validval(str, val, sk .fs .type, st) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, st[r1 -- _type] .type .type, st)), is_indexkey(sk), r ≠ r1 ∨ _type ≠ sk ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- sk, val]), ( 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

[crewrite-arg: validrefkeyval-def , F , [st, val, sk, r, str] → [st, val, sk, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, val, sk, r1, str)]]