Expression of type Forall

from the theory of proveit.numbers.summation

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 a, f, fa, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval, Sum

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f], instance_expr = Forall(instance_param_or_params = [a], instance_expr = Equals(Sum(index_or_indices = [x], summand = fx, domain = Interval(a, a)), fa), domain = Integer))

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())

\forall_{f}~\left[\forall_{a \in \mathbb{Z}}~\left(\left(\sum_{x = a}^{a} f\left(x\right)\right) = f\left(a\right)\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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