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Proof step 146 from proof validrefs-all-same (previous step)

st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), st0[r -- _type] .type ≤ ty, is_array(str, r, st0), 0 < st[r -- _length] .intval, 0 ≤ i, (r = r ∨ r = r1 ∨ r ∈ refs) ∧ r ≠ jvmref → st[r -- _type] = st0[r -- _type] ∧ (is_classtype(st[r -- _type] .type) → (∀ sk. sk ∈ instfields(st[r -- _type] .type .class) → st[r -- sk] = st0[r -- sk])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '])), ∀ r0. (r0 = r ∨ r0 = r1 ∨ r0 ∈ refs) ∧ 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, r1 ' + refs, ty0, st1) ∧ (∀ r0. (r0 = r1 ∨ r0 ∈ refs) ∧ 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, r1 ' + refs, ty0, st2) ⊦ r = jvmref, ¬ st0[r -- _length] .intval ≤ i ∧ is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ validrefs(str, st0[r -- i '] .refval ' + refs, st0[r -- _type] .type .type, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st[r -- i '] = refval(r1), 0 < st0[r -- _length] .intval, is_arraytype(st0[r -- _type] .type), 0 ≤ i, is_array(str, r, st0), is_array(str, r, st), st0[r -- _type] .type ≤ ty, i < st0[r -- _length] .intval, validrefs(str, r1 ' + refs, st0[r -- _type] .type .type, st), ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '], ∀ str0, ty0, st1, st2. validrefs(str0, r1 ' + refs, ty0, st1) ∧ (∀ r0. (r0 = r1 ∨ r0 ∈ refs) ∧ 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, r1 ' + refs, ty0, st2), ∀ r0. (r0 = r ∨ r0 = r1 ∨ r0 ∈ refs) ∧ 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 '])) ⊦ r = jvmref, is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ validrefs(str, st0[r -- i '] .refval ' + refs, st0[r -- _type] .type .type, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]