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Proof step 56 from proof junkref-subspec-samesubclasses (previous step)

is_array(str0, r, st), st[r -- i '] = refval(r0), i < st[r -- _length] .intval, same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(st[r -- _type] .type), is_array(str0, r, st), junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), ∀ str0, str, r1, st0, refs. # refs < # (r0 + refs1) → ( same-subclasses-contains(st0[r1 -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → junkref(str0, r1, st0)) ⊦ r = jvmref, r0 = jvmref, ∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str0, st[r -- i '] .refval, st)), same-subclasses-contains(st[r0 -- _type] .type .jtelemtype .class, str, str0), has_classtype(st[r0 -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
st[r -- i '] = refval(r0), i < st[r -- _length] .intval, same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(st[r -- _type] .type), is_array(str0, r, st), junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), ∀ str0, str, r1, st0, refs. # refs < # (r0 + refs1) → ( same-subclasses-contains(st0[r1 -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → junkref(str0, r1, st0)) ⊦ r = jvmref, r0 = jvmref, same-subclasses-contains(st[r0 -- _type] .type .jtelemtype .class, str, str0), has_classtype(st[r0 -- _type] .type), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str0, st[r -- i0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]