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

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = ExprTuple(Lambda([a, b, c], Conditional(Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(c, x), N), domain = sub_expr1)), N), 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(c + x\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N \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	46, 47, 44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 38
8	Literal
9	ExprTuple	11, 12, 13, 14
10	Operation	operator: 26 operand: 21
11	Operation	operator: 35 operands: 16
12	Operation	operator: 35 operands: 17
13	Operation	operator: 35 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21
16	ExprTuple	46, 22
17	ExprTuple	47, 22
18	ExprTuple	44, 22
19	Literal
20	ExprTuple	38, 23
21	Operation	operator: 24 operand: 28
22	Literal
23	Operation	operator: 26 operand: 39
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	39
28	Lambda	parameter: 45 body: 30
29	ExprTuple	45
30	Conditional	value: 31 condition: 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	45, 39
37	Operation	operator: 40 operands: 41
38	Variable
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	46, 47
44	Variable
45	Variable
46	Variable
47	Variable