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Proof step 5 from proof cyclic-array (previous step)

st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ st[r -- _type] .type .type, is_reftype(st[r -- _type] .type .type), i < st[r -- _length] .intval, is_array(str, r, st) ⊦ validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validrefs(str, refs, ty, st) ∧ ty ≤ ty0 → validrefs(str, refs, ty0, st)

Rule argument

[crewrite-arg: validrefs-superclass , F , [str, refs, ty, st, ty0] → [str, r0 ' + refs0, st[r0 -- _type] .type, st, st[r -- _type] .type .type] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r0 ' + refs0, st[r0 -- _type] .type, st, st[r -- _type] .type .type)]]