Complete proofs by replacing sorry

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
icon
Related questions
Question

Computer Science

Complete proofs by replacing sorry 
import data.set
Luport data.int.basic
open function int set
1
4
section
def f (x : Z) : Z :- x + 3
def g (x : Z) : Z := -x
def h (x : Z) :Z :- 2 * x + 3
6.
8.
9.
10
-- 1
example : injective h :=
11
12
sorry
13
14
example : surjective g :-
15
16
sorry
17
18
-H
example (A B : Type) (u : A + B) (v1 : B + A) (v2 : B + A)
(h1 : left_inverse vi u) (h2 : right_inverse v2 u) : v1 - v2 :-
19
20
21
funext
(assume x,
calc
22
23
vi x - vi (u (v2 x)) : sorry
... - v2 x
24
: sorry)
25
26
end
27
28
-- 4
29
section
30
variables (X Y : Type}
31
variable f : X+ Y
32
variables AB : set x
33
example : f * (A n B) sf" An f 'B :-
34
35
assume y,
assume h1 : yef" (A n B),
show y e f " Anf" B, from sorry
36
37
38
end
39
Transcribed Image Text:import data.set Luport data.int.basic open function int set 1 4 section def f (x : Z) : Z :- x + 3 def g (x : Z) : Z := -x def h (x : Z) :Z :- 2 * x + 3 6. 8. 9. 10 -- 1 example : injective h := 11 12 sorry 13 14 example : surjective g :- 15 16 sorry 17 18 -H example (A B : Type) (u : A + B) (v1 : B + A) (v2 : B + A) (h1 : left_inverse vi u) (h2 : right_inverse v2 u) : v1 - v2 :- 19 20 21 funext (assume x, calc 22 23 vi x - vi (u (v2 x)) : sorry ... - v2 x 24 : sorry) 25 26 end 27 28 -- 4 29 section 30 variables (X Y : Type} 31 variable f : X+ Y 32 variables AB : set x 33 example : f * (A n B) sf" An f 'B :- 34 35 assume y, assume h1 : yef" (A n B), show y e f " Anf" B, from sorry 36 37 38 end 39
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY