Expression of type Conditional

from the theory of proveit.core_expr_types.operations

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, f, n
from proveit.core_expr_types import f__x_1_to_n, f__y_1_to_n, x_1_to_n, y_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f, x_1_to_n, y_1_to_n], instance_expr = Equals(f__x_1_to_n, f__y_1_to_n).with_wrapping_at(2), condition = Equals([x_1_to_n], [y_1_to_n])), InSet(n, Natural))

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\{\forall_{f, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~\left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(\begin{array}{c} \begin{array}{l} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) =  \\ f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \end{array} \end{array}\right) \textrm{ if } n \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	26, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	19, 21, 22
10	Conditional	value: 11 condition: 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 20
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21
19	Variable
20	ExprTuple	22
21	ExprRange	lambda_map: 23 start_index: 25 end_index: 26
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Lambda	parameter: 32 body: 27
24	Lambda	parameter: 32 body: 28
25	Literal
26	Variable
27	IndexedVar	variable: 29 index: 32
28	IndexedVar	variable: 30 index: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable