Expression of type Equals

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

# build up the expression from sub-expressions
sub_expr1 = [n]
expr = Equals(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)])).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} 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) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
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.	()	(2)	('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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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