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Proof step 39 from proof validrefs-subset (previous step)

acc .first = st0[r0 -- mkfs(class, ty1, fieldvar) '] .refval, st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st ⊆ st0, is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), is_referencevalue(st0[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, acc, ty1, st0), ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, acc .first, st2) → validrefs(str0, acc, ty0, st2) ⊦ r0 = jvmref, acc = [], junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ acc .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
acc = r + refs, r = st0[r0 -- mkfs(class, ty1, fieldvar) '] .refval, st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st ⊆ st0, is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), is_referencevalue(st0[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, acc, ty1, st0), ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, acc, ty0, st2) ⊦ r0 = jvmref, acc = [], junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r = st[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc, r, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (acc, r, refs)]]