Expression of type Implies

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 Qx, 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 = 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())

\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)

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.	()	()	('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: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 28 body: 12
10	Operation	operator: 13 operand: 18
11	Operation	operator: 15 operand: 22
12	Conditional	value: 17 condition: 24
13	Literal
14	ExprTuple	18
15	Literal
16	ExprTuple	22
17	Operation	operator: 19 operands: 20
18	Lambda	parameter: 28 body: 21
19	Literal
20	ExprTuple	23, 22
21	Conditional	value: 23 condition: 24
22	Literal
23	Operation	operator: 25 operand: 28
24	Operation	operator: 26 operand: 28
25	Variable
26	Variable
27	ExprTuple	28
28	Variable