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Proof step 40 from proof unchNorec-validrefs (previous step)

st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- _type] .type = mkarraytype(ty0), st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs, ty0, st), 0 ≤ i, 0 < st0[r -- _length] .intval, is_array(str, r, st0), mkarraytype(ty0) ≤ ty, unchangedNorec(r, st, st0), is_array(str, r, st), i < st0[r -- _length] .intval, ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0), ∀ str0, ty1, st1, st2. validrefs(str0, r1 ' + refs, ty1, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, r1 ' + refs, ty1, st2) ⊦ r = jvmref, ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i ∧ is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ validrefs(str, st0[r -- i '] .refval ' + refs, ty0, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- _type] .type = mkarraytype(ty0), st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs, ty0, st), 0 ≤ i, 0 < st0[r -- _length] .intval, is_array(str, r, st0), mkarraytype(ty0) ≤ ty, unchangedNorec(r, st, st0), is_array(str, r, st), i < st0[r -- _length] .intval, ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0), ∀ str0, ty1, st1, st2. validrefs(str0, r1 ' + refs, ty1, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, r1 ' + refs, ty1, st2) ⊦ r = jvmref, is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ validrefs(str, st0[r -- i '] .refval ' + refs, ty0, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]