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 ExprTuple, Function, a, alpha, b, beta, f, g, h, n, theta
from proveit.logic import Exists
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [n]
expr = ExprTuple(Function(f, [Function(g, [a, b]), Exists(instance_param_or_params = sub_expr1, instance_expr = Function(h, sub_expr1), domain = Natural)]), Function(f, [Function(g, [alpha, beta]), Exists(instance_param_or_params = sub_expr1, instance_expr = Function(theta, sub_expr1), domain = 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(f\left(g\left(a, b\right), \exists_{n \in \mathbb{N}}~h\left(n\right)\right), f\left(g\left(\alpha, \beta\right), \exists_{n \in \mathbb{N}}~\theta\left(n\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Variable
5	ExprTuple	8, 9
6	Operation	operator: 12 operands: 10
7	Operation	operator: 14 operand: 18
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operand: 21
10	ExprTuple	16, 17
11	ExprTuple	18
12	Variable
13	ExprTuple	19, 20
14	Literal
15	ExprTuple	21
16	Variable
17	Variable
18	Lambda	parameter: 32 body: 22
19	Variable
20	Variable
21	Lambda	parameter: 32 body: 23
22	Conditional	value: 24 condition: 26
23	Conditional	value: 25 condition: 26
24	Operation	operator: 27 operand: 32
25	Operation	operator: 28 operand: 32
26	Operation	operator: 30 operands: 31
27	Variable
28	Variable
29	ExprTuple	32
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Literal