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, x_eq_y__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 = x_eq_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} = y_{1}\right), \left(x_{2} = y_{2}\right), \ldots, \left(x_{n} = 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	29, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	20, 23, 24
10	Conditional	value: 11 condition: 12
11	Operation	operator: 30 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	ExprRange	lambda_map: 22 start_index: 28 end_index: 29
19	ExprTuple	23
20	Variable
21	ExprTuple	24
22	Lambda	parameter: 37 body: 25
23	ExprRange	lambda_map: 26 start_index: 28 end_index: 29
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Operation	operator: 30 operands: 31
26	Lambda	parameter: 37 body: 32
27	Lambda	parameter: 37 body: 33
28	Literal
29	Variable
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 37
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable