| ¬ (r0 ≠ jvmref ∧ ¬ validref(str, st[r0 -- i '] .refval, ty0, st) ∧ 0 ≤ i ∧ i < st[r0 -- _length] .intval), acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st[r0 -- _type] = typeval(mkarraytype(ty0)), st0[r0 -- _type] = typeval(mkarraytype(ty0)), type∃(str, ty0), i < st0[r0 -- _length] .intval, validrefs(str, r2 ' + refs, ty0, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, r0 ∈ st0, mkarraytype(ty0) ≤ ty, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, r0 -- _type ∈ st0, okarray(r0, ty0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1 |
acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st[r0 -- _type] = typeval(mkarraytype(ty0)), st0[r0 -- _type] = typeval(mkarraytype(ty0)), type∃(str, ty0), i < st0[r0 -- _length] .intval, validrefs(str, r2 ' + refs, ty0, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, r0 ∈ st0, mkarraytype(ty0) ≤ ty, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, r0 -- _type ∈ st0, okarray(r0, ty0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1, ¬ validref(str, st[r0 -- i '] .refval, ty0, st) ∧ ¬ st[r0 -- _length] .intval ≤ i
[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]