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 Function, f, n
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, Sum, one, zero

# build up the expression from sub-expressions
sub_expr1 = [n]
expr = Forall(instance_param_or_params = [f], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Function(f, sub_expr1), domain = Interval(zero, one)), Add(Function(f, [zero]), Function(f, [one]))))

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(\left(\sum_{n = 0}^{1} f\left(n\right)\right) = \left(f\left(0\right) + f\left(1\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 22 body: 5
4	ExprTuple	22
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Lambda	parameter: 26 body: 17
15	Operation	operator: 22 operand: 30
16	Operation	operator: 22 operand: 31
17	Conditional	value: 20 condition: 21
18	ExprTuple	30
19	ExprTuple	31
20	Operation	operator: 22 operand: 26
21	Operation	operator: 24 operands: 25
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Literal