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Proof step 21 from proof junkref-addarray-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 10:
newref(r, st), class∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), tdname+∃(str, class), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ is_arrayref(r, n→i(# vals), addarray(r, mkclasstype(class), vals, st)), r = jvmref
Proof step 20:
newref(r, st), class∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), tdname+∃(str, class), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ 0 ≤ j ∧ j < n→i(# vals) → is_referencevalue(vals[i→n(j)]), r = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]