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, y_1_to_n
from proveit.logic import And, Equals

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