Expression of type Lambda

from the theory of proveit.numbers.modular

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, N, a, b, c, x
from proveit.logic import And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Add, Integer, Interval, Mod, greater_eq, one, subtract, zero

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Lambda([a, b, c], Conditional(Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(x, c), N), domain = sub_expr1), Interval(zero, subtract(N, one))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), greater_eq(Card(sub_expr1), N))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a, b, c\right) \mapsto \left\{\left\{\left(x + c\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}} = \{0~\ldotp \ldotp~N - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  |\{a~\ldotp \ldotp~b\}| \geq N\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	52, 53, 51
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14
9	Operation	operator: 15 operand: 23
10	Operation	operator: 48 operands: 17
11	Operation	operator: 38 operands: 18
12	Operation	operator: 38 operands: 19
13	Operation	operator: 38 operands: 20
14	Operation	operator: 21 operands: 22
15	Literal
16	ExprTuple	23
17	ExprTuple	24, 25
18	ExprTuple	52, 26
19	ExprTuple	53, 26
20	ExprTuple	51, 26
21	Literal
22	ExprTuple	43, 27
23	Lambda	parameter: 50 body: 29
24	Literal
25	Operation	operator: 46 operands: 30
26	Literal
27	Operation	operator: 31 operand: 44
28	ExprTuple	50
29	Conditional	value: 33 condition: 34
30	ExprTuple	43, 35
31	Literal
32	ExprTuple	44
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operand: 45
36	Literal
37	ExprTuple	42, 43
38	Literal
39	ExprTuple	50, 44
40	Literal
41	ExprTuple	45
42	Operation	operator: 46 operands: 47
43	Variable
44	Operation	operator: 48 operands: 49
45	Literal
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	52, 53
50	Variable
51	Variable
52	Variable
53	Variable