Information

1. inv14/WD (true)

(start_xtl_system)
---------------------
radiation ∈ ℤ × ℤ ⇸ ℤ ∧ rover ∈ dom(radiation)

2. reselect_hyp (radiation ∈ field → ℕ)

(reselect_hyp(member($(radiation),total_function($(field),'NATURAL'))))
radiation ∈ field → ℕ
---------------------
radiation ∈ ℤ × ℤ ⇸ ℤ ∧ rover ∈ dom(radiation)

3. reselect_hyp ({rover} ⊆ field)

(reselect_hyp(subset(set_extension([$(rover)]),$(field))))
radiation ∈ field → ℕ
{rover} ⊆ field
---------------------
radiation ∈ ℤ × ℤ ⇸ ℤ ∧ rover ∈ dom(radiation)

4. reselect_hyp (radiation ∈ ℤ × ℤ ⇸ ℤ)

(reselect_hyp(member($(radiation),partial_function(cartesian_product('INTEGER','INTEGER'),'INTEGER'))))
radiation ∈ field → ℕ
{rover} ⊆ field
radiation ∈ ℤ × ℤ ⇸ ℤ
---------------------
radiation ∈ ℤ × ℤ ⇸ ℤ ∧ rover ∈ dom(radiation)

5. and_r

radiation ∈ field → ℕ radiation ∈ field → ℕ
{rover} ⊆ field {rover} ⊆ field
radiation ∈ ℤ × ℤ ⇸ ℤ radiation ∈ ℤ × ℤ ⇸ ℤ
--------------------- ---------------------
radiation ∈ ℤ × ℤ ⇸ ℤ rover ∈ dom(radiation)

6. hyp

radiation ∈ field → ℕ
{rover} ⊆ field
radiation ∈ ℤ × ℤ ⇸ ℤ
---------------------
rover ∈ dom(radiation)

7. DEF_IN_TFCT (radiation ∈ field → ℕ)

(simplify_hyp('DEF_IN_TFCT',member($(radiation),total_function($(field),'NATURAL'))))
radiation ∈ field ⇸ ℕ
dom(radiation) = field
{rover} ⊆ field
radiation ∈ ℤ × ℤ ⇸ ℤ
---------------------
rover ∈ dom(radiation)

8. eq (lr,dom(radiation) = field)

(eq(lr,domain($(radiation)),$(field)))
radiation ∈ field ⇸ ℕ
{rover} ⊆ field
radiation ∈ ℤ × ℤ ⇸ ℤ
---------------------
rover ∈ field

9. SIMP_SUBSETEQ_SING ({rover} ⊆ field)

(simplify_hyp('SIMP_SUBSETEQ_SING',subset(set_extension([$(rover)]),$(field))))
radiation ∈ field ⇸ ℕ
rover ∈ field
radiation ∈ ℤ × ℤ ⇸ ℤ
---------------------
rover ∈ field

10. hyp

Proof of inv14/WD (true) succeeded.