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Proof step 53 from proof validrefs-subset-equiv (previous step)

r ∈ st, is_obj(str, r, st), st[r -- _type] .type ≤ ty, r -- _type ∈ st, is_array(str, r, st0), st ⊆ st0, is_classtype(st[r -- _type] .type), refs = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st0[r -- i ']) ∧ refs .first = st0[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st0), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ is_classtype(st[r -- _type] .type) → ¬ is_array(str, r, st)
Proof step 52:
¬ is_classtype(st0[r -- _type] .type), r ∈ st, is_obj(str, r, st), st[r -- _type] .type ≤ ty, r -- _type ∈ st, is_array(str, r, st0), st ⊆ st0, is_classtype(st[r -- _type] .type), refs = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st0[r -- i ']) ∧ refs .first = st0[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st0), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_classtype(st[r -- _type] .type) → ¬ is_array(str, r, st) ,[st, r, str] → [st0, r, str] ,F ,okfuns , ,is_array-classtype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, r, str)]]