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, x
from proveit.logic import Card, Equals, Forall, InSet, SetOfAll
from proveit.numbers import 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], instance_expr = Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, 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 \in \mathbb{Z}~|~|\{a~\ldotp \ldotp~b\}| \geq N}~\left(\left\{x ~\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: 50 body: 3
2	ExprTuple	50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 46 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	50, 10
9	Lambda	parameters: 55 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 23 operand: 30
19	Operation	operator: 54 operands: 25
20	Operation	operator: 46 operands: 26
21	Operation	operator: 46 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	30
25	ExprTuple	31, 32
26	ExprTuple	56, 33
27	ExprTuple	57, 33
28	Literal
29	ExprTuple	50, 34
30	Lambda	parameter: 51 body: 36
31	Literal
32	Operation	operator: 37 operands: 38
33	Literal
34	Operation	operator: 39 operand: 52
35	ExprTuple	51
36	Conditional	value: 41 condition: 42
37	Literal
38	ExprTuple	50, 43
39	Literal
40	ExprTuple	52
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operands: 47
43	Operation	operator: 48 operand: 53
44	Literal
45	ExprTuple	51, 50
46	Literal
47	ExprTuple	51, 52
48	Literal
49	ExprTuple	53
50	Variable
51	Variable
52	Operation	operator: 54 operands: 55
53	Literal
54	Literal
55	ExprTuple	56, 57
56	Variable
57	Variable