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Proof step 90 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs0 + r1 ', ty1, st), contains(str, st[r0 -- _type] .type ' + tys + st[r1 -- _type] .type ') ⊦ r0 = r1, r1 = jvmref, r = r1, r = jvmref, contains(str, st[r -- _type] .type ' + (st[r0 -- _type] .type ' + tys) + st[r1 -- _type] .type ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ contains(str, ty ' + ty0 ' + tys) ↔ 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) ∧ contains(str, ty0 ' + tys))
Proof step 89:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs0 + r1 ', ty1, st), contains(str, st[r0 -- _type] .type ' + tys + st[r1 -- _type] .type ') ⊦ r0 = r1, 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[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r0 -- _type] .type ≤ ty1 .type) ∧ contains(str, st[r0 -- _type] .type ' + tys + st[r1 -- _type] .type '))

Rule argument

[crewrite-arg: contains-rec , F , [tys, ty0, ty, str] → [tys + st[r1 -- _type] .type ', st[r0 -- _type] .type, st[r -- _type] .type, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (tys + st[r1 -- _type] .type ', st[r0 -- _type] .type, st[r -- _type] .type, str)]]