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Proof step 33 from proof validrefs-levelsubset-01 (previous step)

st[r -- _type] .type ≤ ty, is_array(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, is_obj(str, r, st), ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, refs0 .first, ty, st) → validrefs(str, refs0, ty0, st), refs0 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str0, refs0, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: is_array-arraytype antecedent: succedent: ¬ is_arraytype(st[r -- _type] .type) → ¬ is_array(str, r, st) substlist: [st, r, str] → [st, r, str0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , is_obj-arraytype, ⊦ is_arraytype (st[r -- _type] .type) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st, r, str0)]]