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, Bijections, InSet
from proveit.numbers import Add, Integer, Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, c], Conditional(InSet(Lambda(x, Mod(Add(x, c), N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer)))))

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[x \mapsto \left(\left(x + c\right) ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right] \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z}\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	32, 33, 37
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Lambda	parameter: 36 body: 15
10	Operation	operator: 16 operands: 17
11	Operation	operator: 20 operands: 18
12	Operation	operator: 20 operands: 19
13	Operation	operator: 20 operands: 21
14	ExprTuple	36
15	Operation	operator: 22 operands: 23
16	Literal
17	ExprTuple	24, 25
18	ExprTuple	32, 26
19	ExprTuple	33, 26
20	Literal
21	ExprTuple	37, 26
22	Literal
23	ExprTuple	27, 40
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	Operation	operator: 38 operands: 31
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	34, 35
31	ExprTuple	36, 37
32	Variable
33	Variable
34	Literal
35	Operation	operator: 38 operands: 39
36	Variable
37	Variable
38	Literal
39	ExprTuple	40, 41
40	Variable
41	Operation	operator: 42 operand: 44
42	Literal
43	ExprTuple	44
44	Literal