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Proof step 150 from proof exvalidrefs-03 (conclusion)

¬ junkref(str, r, st), ¬ cyclic(str, r, st), is_obj(str, r, st), r ≠ jvmref, ∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st[r -- _type] .type ≤ fs .type ⊦ ∃ refs. validrefs(str, refs, st[r -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref

User applied rule induction

And obtained the following new goals

Proof step 149:
¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ∧ is_obj(str, r, st) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st[r -- _type] .type ≤ fs .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ ∃ refs. validrefs(str, refs, st[r -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # st .refs, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# st .refs)]]