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

mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r0 -- _type] .type ≤ ty1, is_obj(r, st), validref(str, r, ty, st), validref(str, r0, ty0, st) ⊦ r0 = jvmref, validref(str, r, ty, st[r -- mkfs(class, ty1, fieldvar) ', refval(r0)]), validref(str, r0, st[r0 -- _type] .type, st) ∧ is_reftype(ty1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)
Proof step 5:
¬ ¬ is_reftype(ty1), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r0 -- _type] .type ≤ ty1, is_obj(r, st), validref(str, r, ty, st), validref(str, r0, ty0, st) ⊦ r0 = jvmref, validref(str, r, ty, st[r -- mkfs(class, ty1, fieldvar) ', refval(r0)]), validref(str, r0, st[r0 -- _type] .type, st) ∧ is_reftype(ty1)
Proof step 6:
⊦ ¬ is_reftype(st[r -- _type] .type) ∧ r ≠ jvmref → ¬ validref(str, r, ty, st)

Rule argument

[speclemmaarg: ,¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0) ,[ty0, ty] → [ty1, st[r0 -- _type] .type] ,F ,typefuns , ,le-noreftype-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty1, st[r0 -- _type] .type)]]