Expression of type Lambda

from the theory of proveit.logic.equality

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, P
from proveit.core_expr_types import P__x_1_to_n, P__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import And

# build up the expression from sub-expressions
expr = Lambda([P, x_1_to_n, y_1_to_n], Conditional(P__y_1_to_n, And(P__x_1_to_n, x_eq_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(P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } P\left(x_{1}, x_{2}, \ldots, x_{n}\right), \left(x_{1} = y_{1}\right) ,  \left(x_{2} = y_{2}\right) ,  \ldots ,  \left(x_{n} = 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	12, 15, 8
2	Conditional	value: 3 condition: 4
3	Operation	operator: 12 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	ExprRange	lambda_map: 11 start_index: 18 end_index: 19
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 18 end_index: 19
11	Lambda	parameter: 27 body: 23
12	Variable
13	ExprTuple	15
14	Lambda	parameter: 27 body: 16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 27 body: 22
18	Literal
19	Variable
20	Literal
21	ExprTuple	22, 23
22	IndexedVar	variable: 24 index: 27
23	IndexedVar	variable: 25 index: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable