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, x
from proveit.logic import And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Integer, Interval, LessEq, Mod

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
sub_expr2 = Card(sub_expr1)
expr = ExprTuple(Lambda([a, b], Conditional(Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1)), sub_expr2), And(InSet(a, Integer), InSet(b, Integer), LessEq(sub_expr2, 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\right) \mapsto \left\{|\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = |\{a~\ldotp \ldotp~b\}| \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  |\{a~\ldotp \ldotp~b\}| \leq 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: 38 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 20
7	Literal
8	ExprTuple	10, 11, 12
9	Operation	operator: 23 operand: 18
10	Operation	operator: 32 operands: 14
11	Operation	operator: 32 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18
14	ExprTuple	39, 19
15	ExprTuple	40, 19
16	Literal
17	ExprTuple	20, 34
18	Operation	operator: 21 operand: 25
19	Literal
20	Operation	operator: 23 operand: 36
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	36
25	Lambda	parameter: 35 body: 27
26	ExprTuple	35
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	35, 34
32	Literal
33	ExprTuple	35, 36
34	Variable
35	Variable
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable