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Proof step 23 from proof validrefs-lastelem (previous step)

st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), validrefs(str, r1 ', ty0, st) ⊦ r0 = jvmref, has_reffield(r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_obj(r, st) → (has_reffield(r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_reftype(fs .type)))
Proof step 22:
is_obj(r0, st), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), validrefs(str, r1 ', ty0, st) ⊦ r0 = jvmref, ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_reftype(fs .type)

Rule argument

[speclemmaarg: , is_obj(r, st) → ( has_reffield(r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_reftype(fs .type))) ,[st, r] → [st, r0] ,F ,addfuns , ,has_reffield-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_obj(r, st) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st, r0)]]