Expression of type ExprTuple

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 ExprTuple, Lambda, 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 = ExprTuple(Lambda([f, Q], 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(\left(f, Q\right) \mapsto \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)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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