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, Q__y_1_to_n, y_1_to_n
from proveit.logic import And
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx

# build up the expression from sub-expressions
expr = Lambda([y_1_to_n], Conditional(general_exists_Px_st_Qx, And(P__y_1_to_n, Q__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}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } P\left(y_{1}, y_{2}, \ldots, y_{n}\right) ,  Q\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: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameters: 18 body: 11
9	Operation	operator: 16 operands: 12
10	Operation	operator: 17 operands: 12
11	Conditional	value: 13 condition: 14
12	ExprTuple	15
13	Operation	operator: 16 operands: 18
14	Operation	operator: 17 operands: 18
15	ExprRange	lambda_map: 19 start_index: 23 end_index: 24
16	Variable
17	Variable
18	ExprTuple	20
19	Lambda	parameter: 29 body: 21
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	IndexedVar	variable: 25 index: 29
22	Lambda	parameter: 29 body: 26
23	Literal
24	Variable
25	Variable
26	IndexedVar	variable: 27 index: 29
27	Variable
28	ExprTuple	29
29	Variable