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, Q__x_1_to_m, R__x_1_to_m_y_1_to_n, x_1_to_m, y_1_to_n
from proveit.logic import And

# build up the expression from sub-expressions
expr = Lambda([x_1_to_m, y_1_to_n], Conditional(P__x_1_to_m_y_1_to_n, And(Q__x_1_to_m, 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(x_{1}, x_{2}, \ldots, x_{m}, 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 } Q\left(x_{1}, x_{2}, \ldots, x_{m}\right) ,  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: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 12
3	Operation	operator: 5 operands: 6
4	Variable
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Variable
10	ExprTuple	13
11	Variable
12	ExprTuple	13, 14
13	ExprRange	lambda_map: 15 start_index: 18 end_index: 16
14	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
15	Lambda	parameter: 25 body: 20
16	Variable
17	Lambda	parameter: 25 body: 21
18	Literal
19	Variable
20	IndexedVar	variable: 22 index: 25
21	IndexedVar	variable: 23 index: 25
22	Variable
23	Variable
24	ExprTuple	25
25	Variable