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Proof step 66 from proof validrefs-subset (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
st[r0 -- _length] = st0[r0 -- _length], st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- i '] = refval(r), r0 -- _length ∈ st0, r0 ∈ st0, r0 ∈ st, r0 -- _type ∈ st0, 0 ≤ i, 0 < st0[r0 -- _length] .intval, st0[r0 -- _type] .type ≤ ty, is_array(str, r0, st), is_valid_ref(str, r0, st0), i < st0[r0 -- _length] .intval, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st0), r0 -- _type ∈ st, r0 -- _length ∈ st, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, r ' + refs, ty0, st2), r0 -- i ' ∈ st → r0 -- i ' ∈ st0 ∧ st[r0 -- i '] = refval(r), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, is_referencevalue(st[r0 -- i ']) ∧ r = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st0[r0 -- _type] .type .type, st), is_referencevalue(st[r0 -- i ']) ∧ st[r0 -- i '] .refval ≠ jvmref ∧ (¬ st[st[r0 -- i '] .refval -- _type] .type ≤ st0[r0 -- _type] .type .type ∨ junkref(str, st[r0 -- i '] .refval, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]