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Proof step 15 from proof junkref-addarray-01 (previous step)

0 ≤ j, tdname+∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), class∃(str, class), newref(r, st), j < n→i(# vals), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ r = jvmref, vals = [], is_referencevalue(vals[i→n(j)]), ∃ n. ¬ # vals ≤ n ∧ vals[n] = vals[i→n(j)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n
Proof step 14:
0 ≤ j, 0 ≤ j, tdname+∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), class∃(str, class), newref(r, st), i→n(j) < # vals, ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ r = jvmref, vals = [], is_referencevalue(vals[i→n(j)]), ∃ n. ¬ # vals ≤ n ∧ vals[n] = vals[i→n(j)]

Rule argument

[speclemmaarg: 0 ≤ i ,((* i)) < n→i(n) ↔ i→n(i) < n ,[n, i] → [# vals, j] ,F ,intnat , ,num-n2i-ls-02 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (# vals, j)]]