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 Card, Equals, Forall, InSet, SetOfAll
from proveit.numbers import Add, Integer, Interval, Mod, NaturalPos, greater_eq

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = ExprTuple(Lambda(N, Conditional(Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(x, c), N), domain = sub_expr1)), N), domain = Integer, condition = greater_eq(Card(sub_expr1), N)), InSet(N, NaturalPos))))

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(N \mapsto \left\{\forall_{a, b, c \in \mathbb{Z}~|~|\{a~\ldotp \ldotp~b\}| \geq N}~\left(|\left\{\left(x + c\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N\right) \textrm{ if } N \in \mathbb{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	parameter: 47 body: 3
2	ExprTuple	47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 44 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	47, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	55, 56, 54
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 47
17	Literal
18	ExprTuple	20, 21, 22, 23
19	Operation	operator: 35 operand: 30
20	Operation	operator: 44 operands: 25
21	Operation	operator: 44 operands: 26
22	Operation	operator: 44 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprTuple	30
25	ExprTuple	55, 31
26	ExprTuple	56, 31
27	ExprTuple	54, 31
28	Literal
29	ExprTuple	47, 32
30	Operation	operator: 33 operand: 37
31	Literal
32	Operation	operator: 35 operand: 48
33	Literal
34	ExprTuple	37
35	Literal
36	ExprTuple	48
37	Lambda	parameter: 53 body: 39
38	ExprTuple	53
39	Conditional	value: 40 condition: 41
40	Operation	operator: 42 operands: 43
41	Operation	operator: 44 operands: 45
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	53, 48
46	Operation	operator: 49 operands: 50
47	Variable
48	Operation	operator: 51 operands: 52
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	55, 56
53	Variable
54	Variable
55	Variable
56	Variable