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Proof step 52 from proof validref-refs-last-valid-subset (previous step)

validref(str, st[r0 -- i '] .refval, ty0, st), st0[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _type] = typeval(mkarraytype(ty0)), st0[r0 -- i '] = refval(r2), acc + r1 ' = r2 ' + refs, st0[r0 -- _length] = intval(i0), 0 ≤ i0, 0 < i0, is_arrayref(r0, i0, st0), r0 -- _length ∈ st0, okreftype(refval(r0), mkarraytype(ty0), st0), r0 -- _type ∈ st0, st ⊆ st0, validref(str, r0, mkarraytype(ty0), st), mkarraytype(ty0) ≤ ty, r0 ∈ st0, 0 ≤ i, validrefs(str, r2 ' + refs, ty0, st0), i < i0, type∃(str, ty0), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st0[r0 -- j '], ty0), validref(str, st[r0 -- i '] .refval, st[st[r0 -- i '] .refval -- _type] .type, st) ∧ st ⊆ st0 ∧ st[r0 -- i '] .refval ∈ acc ∧ validrefs(str, acc + r1 ', ty0, st0) → validref(str, r1, st[r1 -- _type] .type, st), ∀ 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 = abstract_type, ty0 .jtelemtype = void_type, validref(str, r1, st[r1 -- _type] .type, st), ¬ r2 ∈ acc ∧ r2 ≠ r1, r1 ≠ r2 ∧ ¬ r1 ∈ refs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
st0[r0 -- _length] = intval(i0), 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 < i0, validrefs(str, r2 ' + refs, ty0, st0), 0 ≤ i, r0 ∈ st0, mkarraytype(ty0) ≤ ty, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, r0 -- _type ∈ st0, okreftype(refval(r0), mkarraytype(ty0), st0), r0 -- _length ∈ st0, is_arrayref(r0, i0, st0), 0 < i0, 0 ≤ i0, validref(str, st[r0 -- i '] .refval, ty0, st), ∀ 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), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st0[r0 -- j '], ty0) ⊦ ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1, validref(str, st[r0 -- i '] .refval, st[st[r0 -- i '] .refval -- _type] .type, st) ∧ st[r0 -- i '] .refval ∈ acc

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]