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Proof step 277 from proof exvalidrefs-maxlength (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), okval(st[r -- 0 '], ty), r -- _type ∈ st, okreftype(refval(r), mkarraytype(ty), st), r -- _length ∈ st, is_arrayref(r, i, st), is_array(str, r, st), r ∈ st, 0 < i, is_reftype(ty) ∨ ty = void_type, ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r = jvmref, 0 = i, is_referencevalue(st[r -- 0 ']), cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st)

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: left 11, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_reftype(ty) → ( okval(val, ty) ↔ is_referencevalue(val))], [CSIMPSEQ : ⊦ okval(val, void_type) ↔ is_referencevalue(val)])]]