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, 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 = ExprTuple(Lambda(f, 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())

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