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 Q, Qx, f, fx, x
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Sum, ZeroSet, zero

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Forall(instance_param_or_params = [f, Q], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(fx, zero), condition = Qx), InSet(Sum(index_or_indices = sub_expr1, summand = fx, condition = Qx), ZeroSet)))

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, Q}~\left(\left[\forall_{x~|~Q\left(x\right)}~\left(f\left(x\right) = 0\right)\right] \Rightarrow \left(\left[\sum_{x~|~Q\left(x\right)}~f\left(x\right)\right] \in \left\{0\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: 9 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	29, 30
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Lambda	parameter: 32 body: 16
14	Operation	operator: 17 operand: 22
15	Operation	operator: 19 operand: 26
16	Conditional	value: 21 condition: 28
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	26
21	Operation	operator: 23 operands: 24
22	Lambda	parameter: 32 body: 25
23	Literal
24	ExprTuple	27, 26
25	Conditional	value: 27 condition: 28
26	Literal
27	Operation	operator: 29 operand: 32
28	Operation	operator: 30 operand: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable