Expression of type Function

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

# build up the expression from sub-expressions
sub_expr1 = [n]
expr = 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())

f\left(g\left(\alpha, \beta\right), \exists_{n \in \mathbb{N}}~\theta\left(n\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Variable
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 11
5	Variable
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Variable
10	Variable
11	Lambda	parameter: 19 body: 12
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Variable
16	ExprTuple	19
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Literal