Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.existence

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
from proveit.core_expr_types import P__y_1_to_n, y_1_to_n
from proveit.logic.booleans.quantification import general_exists_Px

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([y_1_to_n], Conditional(general_exists_Px, P__y_1_to_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(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{\exists_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } P\left(y_{1}, y_{2}, \ldots, y_{n}\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: 7 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 12 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9
8	Lambda	parameters: 13 body: 10
9	ExprRange	lambda_map: 11 start_index: 18 end_index: 19
10	Operation	operator: 12 operands: 13
11	Lambda	parameter: 23 body: 14
12	Variable
13	ExprTuple	15
14	IndexedVar	variable: 16 index: 23
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Variable
17	Lambda	parameter: 23 body: 20
18	Literal
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable