Expression of type Lambda

from the theory of proveit.logic.booleans.quantification

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__x_1_to_m_y_1_to_n, R__x_1_to_m_y_1_to_n, y_1_to_n

# build up the expression from sub-expressions
expr = Lambda([y_1_to_n], Conditional(P__x_1_to_m_y_1_to_n, R__x_1_to_m_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\{P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } R\left(x_{1}, x_{2}, \ldots, x_{m},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: 1 body: 2
1	ExprTuple	9
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 7
4	Operation	operator: 6 operands: 7
5	Variable
6	Variable
7	ExprTuple	8, 9
8	ExprRange	lambda_map: 10 start_index: 13 end_index: 11
9	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
10	Lambda	parameter: 20 body: 15
11	Variable
12	Lambda	parameter: 20 body: 16
13	Literal
14	Variable
15	IndexedVar	variable: 17 index: 20
16	IndexedVar	variable: 18 index: 20
17	Variable
18	Variable
19	ExprTuple	20
20	Variable