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Proof step 19 from proof contains-trans-01 (previous step)

tys + ty0 ' = ty3 ' + tys2, contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, ty3 ' + tys2), is_arraytype(ty2) → ty3 ≤ ty2 .type, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ fs ' ∈ instfields(ty2 .class) ∧ ty3 ≤ fs .type, ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0, ∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ ty3 ≤ fs .type)) ∧ (is_arraytype(ty2) → ty3 ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 ')

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
fs = mkfs(class, ty4, fieldvar), tys + ty0 ' = ty3 ' + tys2, contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, ty3 ' + tys2), is_arraytype(ty2) → ty3 ≤ ty2 .type, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ fs ' ∈ instfields(ty2 .class) ∧ ty3 ≤ ty4, ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0, ∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ ty3 ≤ fs .type)) ∧ (is_arraytype(ty2) → ty3 ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 ')

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class, ty4, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class, ty4, fieldvar)]]