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, f
from proveit.core_expr_types import f__x_1_to_n, f__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import And, Equals

# build up the expression from sub-expressions
expr = Lambda([f, x_1_to_n, y_1_to_n], Conditional(Equals(f__x_1_to_n, f__y_1_to_n), And(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(f, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(x_{1} = y_{1}\right) \land  \left(x_{2} = y_{2}\right) \land  \ldots \land  \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, 16
2	Conditional	value: 3 condition: 4
3	Operation	operator: 22 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 20 end_index: 21
11	ExprTuple	15
12	Variable
13	ExprTuple	16
14	Lambda	parameter: 29 body: 17
15	ExprRange	lambda_map: 18 start_index: 20 end_index: 21
16	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
17	Operation	operator: 22 operands: 23
18	Lambda	parameter: 29 body: 24
19	Lambda	parameter: 29 body: 25
20	Literal
21	Variable
22	Literal
23	ExprTuple	24, 25
24	IndexedVar	variable: 26 index: 29
25	IndexedVar	variable: 27 index: 29
26	Variable
27	Variable
28	ExprTuple	29
29	Variable