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Proof step 7 from proof validref-put-any (previous step)

sk .fs = mkfs(class, ty0, fieldvar), validref(str, r, ty, st), 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])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ validref(str, r, ty, st) ∧ 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])

Rule argument

[crewrite-arg: validref-put-array-any , F , [val, sk, r0, st, ty, r, str] → [val, sk, r0, st, ty, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])], [EXTRATERMS : (val, sk, r0, st, ty, r, str)]]