Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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, Lambda, Variable, a, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, InSet, Set
from proveit.numbers import Add, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_n], Conditional(Equals(Add(a_1_to_n), Mult(x, n)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Set(x)), one, 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_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) = \left(x \cdot n\right) \textrm{ if } \left(a_{1} \in \left\{x\right\}\right) \land  \left(a_{2} \in \left\{x\right\}\right) \land  \ldots \land  \left(a_{n} \in \left\{x\right\}\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: 13 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
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprRange	lambda_map: 16 start_index: 20 end_index: 21
12	Literal
13	ExprTuple	17
14	Literal
15	ExprTuple	31, 21
16	Lambda	parameter: 30 body: 18
17	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
18	Operation	operator: 22 operands: 23
19	Lambda	parameter: 30 body: 24
20	Literal
21	Variable
22	Literal
23	ExprTuple	24, 25
24	IndexedVar	variable: 26 index: 30
25	Operation	operator: 28 operand: 31
26	Variable
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Variable
31	Variable