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 And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Integer, Interval, Mod, greater_eq, one, subtract, zero

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = ExprTuple(Lambda([a, b], Conditional(Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1), Interval(zero, subtract(N, one))), And(InSet(a, Integer), InSet(b, Integer), greater_eq(Card(sub_expr1), N)))))

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\right) \mapsto \left\{\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}} = \{0~\ldotp \ldotp~N - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  |\{a~\ldotp \ldotp~b\}| \geq 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	parameters: 46 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 14 operand: 21
10	Operation	operator: 45 operands: 16
11	Operation	operator: 37 operands: 17
12	Operation	operator: 37 operands: 18
13	Operation	operator: 19 operands: 20
14	Literal
15	ExprTuple	21
16	ExprTuple	22, 23
17	ExprTuple	47, 24
18	ExprTuple	48, 24
19	Literal
20	ExprTuple	41, 25
21	Lambda	parameter: 42 body: 27
22	Literal
23	Operation	operator: 28 operands: 29
24	Literal
25	Operation	operator: 30 operand: 43
26	ExprTuple	42
27	Conditional	value: 32 condition: 33
28	Literal
29	ExprTuple	41, 34
30	Literal
31	ExprTuple	43
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operand: 44
35	Literal
36	ExprTuple	42, 41
37	Literal
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	44
41	Variable
42	Variable
43	Operation	operator: 45 operands: 46
44	Literal
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Variable