Expression of type Lambda

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, Lambda, 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 = Lambda(n, 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())

n \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 31 body: 2
1	ExprTuple	31
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	31, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	22, 25, 26
12	Conditional	value: 13 condition: 14
13	Operation	operator: 32 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	ExprRange	lambda_map: 24 start_index: 30 end_index: 31
21	ExprTuple	25
22	Variable
23	ExprTuple	26
24	Lambda	parameter: 39 body: 27
25	ExprRange	lambda_map: 28 start_index: 30 end_index: 31
26	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
27	Operation	operator: 32 operands: 33
28	Lambda	parameter: 39 body: 34
29	Lambda	parameter: 39 body: 35
30	Literal
31	Variable
32	Literal
33	ExprTuple	34, 35
34	IndexedVar	variable: 36 index: 39
35	IndexedVar	variable: 37 index: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable