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Proof step 42 from proof validrefs-not-contains (previous step)

st[r -- i '] = refval(r0), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r0 ', st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 41:
st[r -- i '] = refval(r0), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, r0 = jvmref ∨ r0 ≠ jvmref ∧ is_valid_ref(str, r0, st) ∧ st[r0 -- _type] .type ≤ st[r -- _type] .type .type, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

Rule argument

[speclemmaarg: , validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty ,[st, ty, r, str] → [st, st[r -- _type] .type .type, r0, str] ,F ,cyclic , ,validrefs-one ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type .type, r0, str)]]