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Proof step 51 from proof contains-field-def-case (previous step)

tys0 ≠ [], type∃(str, ty), ty0 ≤ ty, type∃(str, ty0) ∧ is_reftype(ty0) ∧ (∃ ty1. ty1 ≤ ty0 ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ tys0 .first ≤ fs .type)) ∧ (is_arraytype(ty1) → tys0 .first ≤ ty1 .type) ∧ contains(str, tys0)), is_reftype(tys0 .last), is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ fs ' ∈ instfields(tys0 .last .class), is_arraytype(tys0 .last) → fs ' = _length ⊦ tys0 = [], contains(str, ty ' + tys0), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), contains(str, tys0), is_reftype(tys0 .last), ty1 ≤ ty, is_arraytype(ty1) → tys0 .first ≤ ty1 .type, is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ fs ' ∈ instfields(tys0 .last .class), is_arraytype(tys0 .last) → fs ' = _length, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ fs0 ' ∈ instfields(ty1 .class) ∧ tys0 .first ≤ fs0 .type ⊦ tys0 = [], contains(str, ty ' + tys0), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1])]]