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

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

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, Q\right) \mapsto \left(\left[\forall_{x~|~Q\left(x\right)}~\left(f\left(x\right) \in \mathbb{N}\right)\right] \Rightarrow \left(\left[\sum_{x~|~Q\left(x\right)}~f\left(x\right)\right] \in \mathbb{N}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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