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Proof step 109 from proof validrefs-all-same (previous step)

st[r -- _type] = typeval(mkarraytype(ty1)), st[r -- _length] = st0[r -- _length], st0[r -- _type] = typeval(mkarraytype(ty1)), 0 ≤ st0[r -- _length] .intval, is_arrayref(r, st0[r -- _length] .intval, st), r -- _length ∈ st, okreftype(refval(r), mkarraytype(ty1), st), type∃(str, ty1), r -- _type ∈ st0, r ∈ st0, r ∈ st, mkarraytype(ty1) ≤ ty, r -- _type ∈ st, is_integervalue(st0[r -- _length]), r -- _length ∈ st0, ∀ j0. ¬ j0 < 0 ∧ ¬ st0[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty1), ∀ 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 '])), ∀ 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), refs0 = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '] ⊦ r = jvmref, ty1 .jtelemtype = void_type, ty1 .jtelemtype = abstract_type, validrefs(str, r ' + refs0, ty, st0), (0 ≤ j ∧ j < st0[r -- _length] .intval → okval(st0[r -- j '], ty1)) ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ okreftype(refval(r), mkarraytype(ty1), st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 108:
st0[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty1)), st[r -- _length] = st0[r -- _length], st0[r -- _type] = typeval(mkarraytype(ty1)), 0 ≤ i0, is_arrayref(r, i0, st), r -- _length ∈ st, okreftype(refval(r), mkarraytype(ty1), st), type∃(str, ty1), r -- _type ∈ st0, r ∈ st0, r ∈ st, mkarraytype(ty1) ≤ ty, r -- _type ∈ st, is_integervalue(st0[r -- _length]), r -- _length ∈ st0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty1), ∀ 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 '])), ∀ 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), refs0 = [] ∨ 0 ≤ i ∧ i < i0 ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ i. ¬ i < 0 ∧ ¬ i0 ≤ i → st[r -- i '] = st0[r -- i '] ⊦ r = jvmref, ty1 .jtelemtype = void_type, ty1 .jtelemtype = abstract_type, validrefs(str, r ' + refs0, ty, st0), (0 ≤ j ∧ j < i0 → okval(st0[r -- j '], ty1)) ∧ is_arrayref(r, i0, st0) ∧ okreftype(refval(r), mkarraytype(ty1), st0)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-02 antecedent: succedent: is_integervalue(val) → (i = val .intval ↔ val = intval(i)) substlist: [val, i] → [st0[r -- _length], i0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st0[r -- _length], i0)]]