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Proof step 10 from proof junkrefs-put-badfield (previous step)

st[r -- _type] .type ≤ ty, junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), is_obj(str, r, st), ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type), r ≠ r0 ∨ _type ≠ fs ' ⊦ r = jvmref, junkrefs(str, r ' + acc, ty, st), is_obj(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 9:
r -- _type ≠ r0 -- fs ', st[r -- _type] .type ≤ ty, junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), is_obj(str, r, st), ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type), r ≠ r0 ∨ _type ≠ fs ' ⊦ r = jvmref, junkrefs(str, r ' + acc, ty, st), is_obj(str, r, st[r0 -- fs ', val]) ∧ st[r -- _type] .type ≤ ty, is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- _type, val, r0 -- fs ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (r -- _type, val, r0 -- fs ', st)]]