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Proof step 30 from proof junkrefs-put-badfield (previous step)

is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']), fs0 ' ∈ instfields((st[r0 -- fs ', val][r -- _type]) .type .class), is_obj(str, r, st), (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, junkrefs(str, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, fs0 .type, st[r0 -- fs ', val]), ∀ str0, ty0, st0, r1, fs1, val0. junkrefs(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty0, st0[r1 -- fs1 ', val0]) → junkrefs(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty0, st0) ∨ is_typevalue(st0[r1 -- _type]) ∧ is_reftype(st0[r1 -- _type] .type) ⊦ r = jvmref, junkrefs(str, r ' + (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
fs0 = mkfs(class, ty1, fieldvar), is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']), fs0 ' ∈ instfields((st[r0 -- fs ', val][r -- _type]) .type .class), is_obj(str, r, st), (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, junkrefs(str, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty1, st[r0 -- fs ', val]), ∀ str0, ty0, st0, r1, fs1, val0. junkrefs(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty0, st0[r1 -- fs1 ', val0]) → junkrefs(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty0, st0) ∨ is_typevalue(st0[r1 -- _type]) ∧ is_reftype(st0[r1 -- _type] .type) ⊦ r = jvmref, junkrefs(str, r ' + (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs0, class, ty1, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs0, class, ty1, fieldvar)]]