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Proof step 8 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])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ is_referencevalue(val) ∧ validref(str, r, ty, st) ∧ okval(val, st[r1 -- _type] .type .type) → validref(str, r, ty, st[r1 -- i ', val])
Proof step 7:
¬ (¬ is_referencevalue(val) ∧ validref(str, r, ty, st) ∧ okval(val, 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])

Rule argument

[crewrite-arg: validref-put-array-norefval , F , [val, i, r1, st, ty, r, str] → [val, i, r0, st, ty, r, str] ]

Additional information

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