| acc + r0 ' = r4 ' + refs, st[r1 -- i '] = refval(r4), i < st[r1 -- _length] .intval, validrefs(str, r4 ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), is_array(str, r1, st), r ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(val, ty1), st[r1 -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ mkfs(class, ty1, fieldvar) ' = _type, mkfs(class, ty1, fieldvar) ' = _length, r1 = jvmref, r = r1, r ∈ acc, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r4 = st[r1 -- i0 '] .refval ∧ validrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st), r0 ≠ r4 ∧ ¬ r0 ∈ refs, ¬ r4 ∈ acc ∧ r4 ≠ r0 |
acc + r0 ' = r4 ' + refs, st[r1 -- i '] = refval(r4), i < st[r1 -- _length] .intval, validrefs(str, r4 ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), is_array(str, r1, st), r ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(val, ty1), st[r1 -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ mkfs(class, ty1, fieldvar) ' = _type, mkfs(class, ty1, fieldvar) ' = _length, r1 = jvmref, r = r1, r ∈ acc, ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r4 = st[r1 -- i '] .refval ∧ validrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st), r0 ≠ r4 ∧ ¬ r0 ∈ refs, ¬ r4 ∈ acc ∧ r4 ≠ r0
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i)]]