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, ExprRange, ExprTuple, IndexedVar, L, Lambda, Variable, a, b, c, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Mod, ModAbs, Real, RealPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j], Conditional(Forall(instance_param_or_params = [L], instance_expr = Equals(ModAbs(Add(a_1_to_i, Mod(b, L), c_1_to_j), L), ModAbs(Add(a_1_to_i, b, c_1_to_j), L)).with_wrapping_at(2), domain = RealPos), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Real), one, i), InSet(b, Real), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Real), one, j)))))

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_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}\right) \mapsto \left\{\forall_{L \in \mathbb{R}^+}~\left(\begin{array}{c} \begin{array}{l} \left|a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b ~\textup{mod}~ L\right)+ c_{1} +  c_{2} +  \ldots +  c_{j}\right|_{\textup{mod}\thinspace L} =  \\ \left|a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right|_{\textup{mod}\thinspace L} \end{array} \end{array}\right) \textrm{ if } \left(a_{1} \in \mathbb{R}\right) ,  \left(a_{2} \in \mathbb{R}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{R}\right) ,  b \in \mathbb{R}, \left(c_{1} \in \mathbb{R}\right) ,  \left(c_{2} \in \mathbb{R}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{R}\right)\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: 39 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameter: 51 body: 14
10	ExprRange	lambda_map: 15 start_index: 48 end_index: 46
11	Operation	operator: 26 operands: 16
12	ExprRange	lambda_map: 17 start_index: 48 end_index: 49
13	ExprTuple	51
14	Conditional	value: 18 condition: 19
15	Lambda	parameter: 57 body: 20
16	ExprTuple	50, 31
17	Lambda	parameter: 57 body: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 26 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 29
24	ExprTuple	51, 30
25	ExprTuple	52, 31
26	Literal
27	ExprTuple	53, 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	Literal
32	ExprTuple	35, 51
33	Literal
34	ExprTuple	36, 51
35	Operation	operator: 38 operands: 37
36	Operation	operator: 38 operands: 39
37	ExprTuple	41, 40, 42
38	Literal
39	ExprTuple	41, 50, 42
40	Operation	operator: 43 operands: 44
41	ExprRange	lambda_map: 45 start_index: 48 end_index: 46
42	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
43	Literal
44	ExprTuple	50, 51
45	Lambda	parameter: 57 body: 52
46	Variable
47	Lambda	parameter: 57 body: 53
48	Literal
49	Variable
50	Variable
51	Variable
52	IndexedVar	variable: 54 index: 57
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable