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Proof step 69 from proof validrefs-set-null (conclusion)

⊦ validrefs(str, refs + refs0, ty, st) ∧ ¬ dups(refs) ∧ refs ≠ [] ∧ is_obj(str, refs .last, st) ∧ fs ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_reftype(fs .type) ∧ refs0 ≠ [] → validrefs(str, refs + jvmref ', ty, st[refs .last -- fs ', refval(jvmref)])

User applied rule structural induction

And obtained the following new goals

Proof step 68:
∀ str, refs0, ty, st, fs. validrefs(str, acc + refs0, ty, st) ∧ ¬ dups(acc) ∧ acc ≠ [] ∧ is_obj(str, acc .last, st) ∧ fs ' ∈ instfields(st[acc .last -- _type] .type .class) ∧ is_reftype(fs .type) ∧ refs0 ≠ [] → validrefs(str, acc + jvmref ', ty, st[acc .last -- fs ', refval(jvmref)]) ⊦ validrefs(str, (r + acc) + refs0, ty, st) ∧ ¬ dups(r + acc) ∧ r + acc ≠ [] ∧ is_obj(str, (r + acc) .last, st) ∧ fs ' ∈ instfields(st[(r + acc) .last -- _type] .type .class) ∧ is_reftype(fs .type) ∧ refs0 ≠ [] → validrefs(str, (r + acc) + jvmref ', ty, st[(r + acc) .last -- fs ', refval(jvmref)])

Rule argument

[VARWITHVARSEQSARG : refs, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : references generated by [], +;])]]