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

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Lambda([a, b], Conditional(Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1)), N), And(InSet(a, Integer), InSet(b, 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\right) \mapsto \left\{|\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N \textrm{ if } a \in \mathbb{Z} ,  b \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: 37 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 33
6	Literal
7	ExprTuple	9, 10, 11
8	Operation	operator: 22 operand: 17
9	Operation	operator: 31 operands: 13
10	Operation	operator: 31 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17
13	ExprTuple	38, 18
14	ExprTuple	39, 18
15	Literal
16	ExprTuple	33, 19
17	Operation	operator: 20 operand: 24
18	Literal
19	Operation	operator: 22 operand: 35
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	35
24	Lambda	parameter: 34 body: 26
25	ExprTuple	34
26	Conditional	value: 27 condition: 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	34, 33
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable