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 Equals, Forall, Implies, InSet
from proveit.numbers import Sum, ZeroSet, zero

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = 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(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)

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