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Proof step 22 from proof cyclic-addarray-this-01 (previous step)

validrefs(str, r1 ' + refs, ty, addarray(r0, ty, vals, st)), 0 ≤ i, is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), i < n→i(# vals), # vals ≤ i→n(i), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ vals = [], r0 = jvmref, vals[i→n(i)] ∈ vals, r0 ≠ r1 ∧ ¬ r0 ∈ refs ∧ ¬ r1 ∈ refs ∧ ¬ dups(refs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
0 ≤ i ⊦ ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i

Rule argument

[speclemmaarg: 0 ≤ i ,((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i ,[i, m] → [i, # vals] ,F ,intnat , ,num-i2n-le-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i, # vals)]]