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Proof step 6 from proof contains-intarray-01 (previous step)

⊦ (∃ ty. is_arraytype(ty) ∧ ty .type = int_type ∧ type∃(str, ty) ∧ ty0 ≤ ty .type ∧ contains(str, ty0 ' + tys0)) ↔ ty0 ' + tys0 = int_type '

User applied rule case distinction

And obtained the following new goals

Proof step 2:
⊦ contains(str, int_type ' + tys) ↔ tys = []
Proof step 5:
ty0 ' + tys0 = int_type ' ⊦ ∃ ty. is_arraytype(ty) ∧ ty .type = int_type ∧ type∃(str, ty) ∧ ty0 ≤ ty .type ∧ contains(str, ty0 ' + tys0)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ int_type ↔ ty = int_type], [CSIMPSEQ : ⊦ ty ' = ty0 ' + tys ↔ ty = ty0 ∧ tys = []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])]]