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Proof step 19 from proof contains-field-def-case (previous step)

is_reftype(ty), ty1 ≤ ty, type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), type∃(str, ty2), is_reftype(ty2), is_classtype(ty1), mkfs(class, ty3, fieldvar) ' ∈ instfields(ty1 .class), ty2 ≤ ty3, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ fs ' ∈ instfields(ty2 .class), is_arraytype(ty2) → fs ' = _length ⊦ ty2 ≤ ty, interface∃(str, ty1 .class), ∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1
Proof step 18:
ty1 ≤ ty0 ∧ ty0 ≤ ty, is_reftype(ty), true, type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), type∃(str, ty2), is_reftype(ty2), is_classtype(ty1), mkfs(class, ty3, fieldvar) ' ∈ instfields(ty1 .class), ty2 ≤ ty3, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ fs ' ∈ instfields(ty2 .class), is_arraytype(ty2) → fs ' = _length ⊦ ty2 ≤ ty, interface∃(str, ty1 .class), ∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type

Rule argument

[speclemmaarg: ,ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1 ,[ty, ty0, ty1] → [ty1, ty0, ty] ,F ,typefuns , ,transitivity ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty1, ty0, ty)]]