Expression of type ExprTuple

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, ExprTuple, 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 NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(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), condition = x_eq_y__1_to_n), InSet(n, NaturalPos))))

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(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(f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = f\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right) \textrm{ if } n \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 32 body: 3
2	ExprTuple	32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	32, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	23, 26, 27
13	Conditional	value: 14 condition: 15
14	Operation	operator: 33 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	ExprRange	lambda_map: 25 start_index: 31 end_index: 32
22	ExprTuple	26
23	Variable
24	ExprTuple	27
25	Lambda	parameter: 40 body: 28
26	ExprRange	lambda_map: 29 start_index: 31 end_index: 32
27	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
28	Operation	operator: 33 operands: 34
29	Lambda	parameter: 40 body: 35
30	Lambda	parameter: 40 body: 36
31	Literal
32	Variable
33	Literal
34	ExprTuple	35, 36
35	IndexedVar	variable: 37 index: 40
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable