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Proof step 40 from proof junkrefs-addarray (previous step)

(addarray(r0, ty0, vals, st)[r -- i ']) = refval(r2), junkrefs(str, r2 ' + refs, (addarray(r0, ty0, vals, st)[r -- _type]) .type .type, addarray(r0, ty0, vals, st)), i < (addarray(r0, ty0, vals, st)[r -- _length]) .intval, is_array(str, r, st), (addarray(r0, ty0, vals, st)[r -- _type]) .type ≤ ty, is_array(str, r, addarray(r0, ty0, vals, st)), 0 < (addarray(r0, ty0, vals, st)[r -- _length]) .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, newref(r0, st), ∀ str0, ty1, r1, ty2, vals0, st0. junkrefs(str0, r2 ' + refs, ty1, addarray(r1, ty2, vals0, st0)) ∧ newref(r1, st0) → r1 = jvmref ∨ junkrefs(str0, r2 ' + refs, ty1, st0) ⊦ r0 = jvmref, r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk] ,[rk, st, vals, ty, r] → [r -- _type, st, vals, ty0, r0] ,F ,addarray , ,add-at-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(ty))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _length ] ) = intval(n→i(# vals))], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st) [r -- i ' ] ) = vals[i→n(i)]], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ newref(r, st) → ¬ is_array(str, r, st)])], [EXTRATERMS : (r -- _type, st, vals, ty0, r0)]]