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Proof step 15 from proof validrefs-set-null (previous step)

refs0 .first = st[r -- fs0 '] .refval, validrefs(str, refs0, fs0 .type, st), is_referencevalue(st[r -- fs0 ']), fs0 ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_reftype(fs .type), is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class) ⊦ refs0 = [], r = jvmref, _type = fs ', validrefs(str, r ' + jvmref ', ty, st[r -- fs ', refval(jvmref)]), is_obj(str, r, st[r -- fs ', refval(jvmref)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
refs0 = r0 + refs, r0 = st[r -- fs0 '] .refval, validrefs(str, refs0, fs0 .type, st), is_referencevalue(st[r -- fs0 ']), fs0 ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_reftype(fs .type), is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class) ⊦ refs0 = [], r = jvmref, _type = fs ', validrefs(str, r ' + jvmref ', ty, st[r -- fs ', refval(jvmref)]), is_obj(str, r, st[r -- fs ', refval(jvmref)])

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r0, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r0, refs)]]