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Proof step 26 from proof contains-field-def-case (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ contains(str, ty ') ↔ type∃(str, ty)
Proof step 25:
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_arraytype(ty1) → ty2 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ 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 ⊦ contains(str, ty ' + ty2 '), ty2 ≤ ty

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ' .last = ty], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ tys + [] = tys])]]