Expression of type ExprTuple

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, ExprTuple, Lambda, f, g
from proveit.core_expr_types import f__x_1_to_n, g__x_1_to_n, x_1_to_n
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, g, x_1_to_n], Conditional(Equals(f__x_1_to_n, g__x_1_to_n), Equals(f, g))))

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(\left(f, g, x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = g\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } f = g\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	parameters: 2 body: 3
2	ExprTuple	11, 12, 14
3	Conditional	value: 4 condition: 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 11 operands: 13
10	Operation	operator: 12 operands: 13
11	Variable
12	Variable
13	ExprTuple	14
14	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
15	Lambda	parameter: 21 body: 18
16	Literal
17	Variable
18	IndexedVar	variable: 19 index: 21
19	Variable
20	ExprTuple	21
21	Variable