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, one, subtract, zero

# 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(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(x, c), N), domain = sub_expr1), Interval(zero, subtract(N, one))), 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\}} = \{0~\ldotp \ldotp~N - 1\}\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: 53 body: 3
2	ExprTuple	53
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 48 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	53, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	62, 63, 61
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23, 24
19	Operation	operator: 25 operand: 33
20	Operation	operator: 58 operands: 27
21	Operation	operator: 48 operands: 28
22	Operation	operator: 48 operands: 29
23	Operation	operator: 48 operands: 30
24	Operation	operator: 31 operands: 32
25	Literal
26	ExprTuple	33
27	ExprTuple	34, 35
28	ExprTuple	62, 36
29	ExprTuple	63, 36
30	ExprTuple	61, 36
31	Literal
32	ExprTuple	53, 37
33	Lambda	parameter: 60 body: 39
34	Literal
35	Operation	operator: 56 operands: 40
36	Literal
37	Operation	operator: 41 operand: 54
38	ExprTuple	60
39	Conditional	value: 43 condition: 44
40	ExprTuple	53, 45
41	Literal
42	ExprTuple	54
43	Operation	operator: 46 operands: 47
44	Operation	operator: 48 operands: 49
45	Operation	operator: 50 operand: 55
46	Literal
47	ExprTuple	52, 53
48	Literal
49	ExprTuple	60, 54
50	Literal
51	ExprTuple	55
52	Operation	operator: 56 operands: 57
53	Variable
54	Operation	operator: 58 operands: 59
55	Literal
56	Literal
57	ExprTuple	60, 61
58	Literal
59	ExprTuple	62, 63
60	Variable
61	Variable
62	Variable
63	Variable