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Proof step 48 from proof junkrefs-put-null (previous step)

mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, junkrefs (str, st[r0 -- i '] .refval ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), ∀ str0, ty1, st0, r1, fs. ¬ junkrefs(str0, st[r0 -- i '] .refval ' + refs, ty1, st0) ∧ is_obj(r1, st0) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st0[r1 -- _type] .type .class) → ¬ junkrefs(str0, st[r0 -- i '] .refval ' + refs, ty1, st0[r1 -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, junkrefs(str, r0 ' + st[r0 -- i '] .refval ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
st[r0 -- i '] = refval(r2), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, junkrefs (str, r2 ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), ∀ str0, ty1, st0, r1, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_obj(r1, st0) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st0[r1 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, junkrefs(str, r0 ' + r2 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r0 -- i '], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- i '], r2)]]