Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 6 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 11 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8
7	Lambda	parameters: 12 body: 9
8	ExprRange	lambda_map: 10 start_index: 17 end_index: 18
9	Operation	operator: 11 operands: 12
10	Lambda	parameter: 22 body: 13
11	Variable
12	ExprTuple	14
13	IndexedVar	variable: 15 index: 22
14	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
15	Variable
16	Lambda	parameter: 22 body: 19
17	Literal
18	Variable
19	IndexedVar	variable: 20 index: 22
20	Variable
21	ExprTuple	22
22	Variable