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Proof step 97 from proof validrefs-all-same (previous step)

st0[r -- _type] = typeval(mkarraytype(ty1)), st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty1)), st0[r -- _length] = intval(i0), j < i0, 0 ≤ i0, r -- _length ∈ st0, r -- _type ∈ st, mkarraytype(ty1) ≤ ty, r ∈ st, r ∈ st0, r -- _type ∈ st0, type∃(str, ty1), r -- _length ∈ st, 0 ≤ j, 0 < i0, ∀ i. ¬ i < 0 ∧ ¬ i0 ≤ i → st[r -- i '] = st0[r -- i '], refs0 = [] ∨ 0 ≤ i ∧ i < i0 ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ str0, ty0, st1, st2. validrefs(str0, refs0, ty0, st1) ∧ (∀ r0. r0 ∈ refs0 ∧ r0 ≠ jvmref → st1[r0 -- _type] = st2[r0 -- _type] ∧ (is_classtype(st1[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st1[r0 -- _type] .type .class) → st1[r0 -- sk] = st2[r0 -- sk])) ∧ ( is_arraytype(st1[r0 -- _type] .type) → st1[r0 -- _length] = st2[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st1[r0 -- _length] .intval → st1[r0 -- i '] = st2[r0 -- i ']))) → validrefs(str0, refs0, ty0, st2), ∀ r0. (r0 = r ∨ r0 ∈ refs0) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty1), ¬ j < 0 ∧ ¬ i0 ≤ j → r -- j ' ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → r -- j0 ' ∈ st ⊦ ty1 .jtelemtype = abstract_type, ty1 .jtelemtype = void_type, r = jvmref, r -- j ' ∈ st0, validrefs(str, r ' + refs0, ty, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
st0[r -- _type] = typeval(mkarraytype(ty1)), st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty1)), st0[r -- _length] = intval(i0), j < i0, 0 ≤ i0, r -- _length ∈ st0, r -- _type ∈ st, mkarraytype(ty1) ≤ ty, r ∈ st, r ∈ st0, r -- _type ∈ st0, type∃(str, ty1), r -- _length ∈ st, 0 ≤ j, 0 < i0, r -- j ' ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → r -- j0 ' ∈ st, ∀ i. ¬ i < 0 ∧ ¬ i0 ≤ i → st[r -- i '] = st0[r -- i '], refs0 = [] ∨ 0 ≤ i ∧ i < i0 ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ str0, ty0, st1, st2. validrefs(str0, refs0, ty0, st1) ∧ (∀ r0. r0 ∈ refs0 ∧ r0 ≠ jvmref → st1[r0 -- _type] = st2[r0 -- _type] ∧ (is_classtype(st1[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st1[r0 -- _type] .type .class) → st1[r0 -- sk] = st2[r0 -- sk])) ∧ ( is_arraytype(st1[r0 -- _type] .type) → st1[r0 -- _length] = st2[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st1[r0 -- _length] .intval → st1[r0 -- i '] = st2[r0 -- i ']))) → validrefs(str0, refs0, ty0, st2), ∀ r0. (r0 = r ∨ r0 ∈ refs0) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty1) ⊦ ty1 .jtelemtype = abstract_type, ty1 .jtelemtype = void_type, r = jvmref, r -- j ' ∈ st0, validrefs(str, r ' + refs0, ty, st0)

Rule argument

[emptyarg]

Additional information

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