Expression of type Lambda

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 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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