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Proof step 54 from proof junkrefs-union (previous step)

r -- _length ∈ st, (st0 ∪ st)[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs, (st0 ∪ st)[r -- _type] .type .type, st0 ∪ st), i < st[r -- _length] .intval, is_array(str, r, st), (st0 ∪ st)[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. junkrefs(str0, r0 ' + refs, ty0, st1 ∪ st2) → junkrefs(str0, r0 ' + refs, ty0, st2) ⊦ r = jvmref, ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ junkrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
(st0 ∪ st)[r -- i '] = refval(r0), r -- _length ∈ st, junkrefs(str, r0 ' + refs, (st0 ∪ st)[r -- _type] .type .type, st0 ∪ st), i < st[r -- _length] .intval, is_array(str, r, st), (st0 ∪ st)[r -- _type] .type ≤ ty, 0 ≤ i, st[r -- _type] .type ≤ ty, r ∈ st, 0 < st[r -- _length] .intval, ∀ str0, ty0, st1, st2. junkrefs(str0, r0 ' + refs, ty0, st1 ∪ st2) → junkrefs(str0, r0 ' + refs, ty0, st2) ⊦ r = jvmref, is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ junkrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])]]