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Proof step 6 from proof validref-put-array-any (previous step)

validref(str, r, ty, st), ¬ is_referencevalue(val) → okval(val, st[r0 -- _type] .type .type), 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)) ⊦ validref(str, r, ty, st[r0 -- i ', val]), ¬ is_referencevalue(val) ∧ okval(val, st[r0 -- _type] .type .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ validref(str, r, ty0, st) ∧ validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ is_referencevalue(val) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type)) → validref(str, r, ty0, st[r0 -- i ', val])
Proof step 5:
¬ ( validref(str, r, ty, st) ∧ validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ is_referencevalue(val) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type))), validref(str, r, ty, st), ¬ is_referencevalue(val) → okval(val, st[r0 -- _type] .type .type), 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)) ⊦ validref(str, r, ty, st[r0 -- i ', val]), ¬ is_referencevalue(val) ∧ okval(val, st[r0 -- _type] .type .type)

Rule argument

[crewrite-arg: validref-put-array-refval-02 , F , [val, i, r0, st, ty0, r, str] → [val, i, r0, st, ty, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, i, r0, st, ty, r, str)]]