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Proof step 114 from proof validrefs-not-contains (previous step)

st[r -- i '] = refval(r1), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs0 + r1 ', st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ r1 = jvmref, r = r1, r = jvmref, contains(str, st[r -- _type] .type ' + st[r1 -- _type] .type ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 108:
⊦ contains(str, ty ' + ty0 ') ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type) ∧ type∃(str, ty0))
Proof step 113:
st[r -- i '] = refval(r1), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs0 + r1 ', st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ r1 = jvmref, r = r1, r = jvmref, type∃(str, st[r -- _type] .type) ∧ is_reftype(st[r -- _type] .type) ∧ (∃ ty1. ty1 ≤ st[r -- _type] .type ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ st[r1 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r1 -- _type] .type ≤ ty1 .type) ∧ type∃(str, st[r1 -- _type] .type))

Rule argument

[crewrite-arg: contains-two , F , [ty0, ty, str] → [st[r1 -- _type] .type, st[r -- _type] .type, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r1 -- _type] .type, st[r -- _type] .type, str)]]