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, P, n
from proveit.core_expr_types import P__x_1_to_n, P__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 = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [P, x_1_to_n, y_1_to_n], instance_expr = P__y_1_to_n, conditions = [P__x_1_to_n, 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(n \mapsto \left\{\forall_{P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~P\left(x_{1}, x_{2}, \ldots, x_{n}\right), \left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\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: 30 body: 3
2	ExprTuple	30
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	30, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	20, 25, 26
13	Conditional	value: 14 condition: 15
14	Operation	operator: 20 operands: 24
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 23
19	Operation	operator: 21 operands: 22
20	Variable
21	Literal
22	ExprTuple	23, 24
23	ExprTuple	25
24	ExprTuple	26
25	ExprRange	lambda_map: 27 start_index: 29 end_index: 30
26	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
27	Lambda	parameter: 36 body: 31
28	Lambda	parameter: 36 body: 32
29	Literal
30	Variable
31	IndexedVar	variable: 33 index: 36
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable