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 ExprTuple, Lambda, N, a, b, x
from proveit.logic import Bijections
from proveit.numbers import Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(x, Mod(x, N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one))))

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(x \mapsto \left(x ~\textup{mod}~ N\right), \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Lambda	parameter: 11 body: 4
2	Operation	operator: 5 operands: 6
3	ExprTuple	11
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 21
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Variable
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Variable
16	Variable
17	Literal
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Operation	operator: 23 operand: 25
23	Literal
24	ExprTuple	25
25	Literal