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Proof step 59 from proof junkref-addarray-01 (previous step)

is_array(str, r, addarray(r, ty, vals, st)) ∧ (addarray(r, ty, vals, st)[r -- _type]) .type ≤ mkarraytype(ty), newref(r, st), is_classtype(ty), class∃(str, ty .class), refs0 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (addarray(r, ty, vals, st)[r -- _length]) .intval ∧ is_referencevalue(addarray(r, ty, vals, st)[r -- i ']) ∧ refs0 .first = (addarray(r, ty, vals, st)[r -- i ']) .refval ∧ junkrefs(str, refs0, (addarray(r, ty, vals, st)[r -- _type]) .type .type, addarray(r, ty, vals, st))), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
refs0 .first = vals[i→n(i)] .refval, 0 ≤ i, junkrefs(str, refs0, ty, addarray(r, ty, vals, st)), is_referencevalue(vals[i→n(i)]), i < n→i(# vals), class∃(str, ty .class), is_classtype(ty), newref(r, st), is_array(str, r, addarray(r, ty, vals, st)), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ refs0 = [], r = jvmref, vals = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st) [r -- i ' ] ) = vals[i→n(i)]], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _length ] ) = intval(n→i(# vals))], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(ty))])]]