Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	53, 54, 52
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14, 15
10	Operation	operator: 16 operand: 24
11	Operation	operator: 49 operands: 18
12	Operation	operator: 39 operands: 19
13	Operation	operator: 39 operands: 20
14	Operation	operator: 39 operands: 21
15	Operation	operator: 22 operands: 23
16	Literal
17	ExprTuple	24
18	ExprTuple	25, 26
19	ExprTuple	53, 27
20	ExprTuple	54, 27
21	ExprTuple	52, 27
22	Literal
23	ExprTuple	44, 28
24	Lambda	parameter: 51 body: 30
25	Literal
26	Operation	operator: 47 operands: 31
27	Literal
28	Operation	operator: 32 operand: 45
29	ExprTuple	51
30	Conditional	value: 34 condition: 35
31	ExprTuple	44, 36
32	Literal
33	ExprTuple	45
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operand: 46
37	Literal
38	ExprTuple	43, 44
39	Literal
40	ExprTuple	51, 45
41	Literal
42	ExprTuple	46
43	Operation	operator: 47 operands: 48
44	Variable
45	Operation	operator: 49 operands: 50
46	Literal
47	Literal
48	ExprTuple	51, 52
49	Literal
50	ExprTuple	53, 54
51	Variable
52	Variable
53	Variable
54	Variable