Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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 Conditional, Lambda, P, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Forall, Set

# build up the expression from sub-expressions
expr = Lambda(P, Conditional(And(Pk_a1_to_an), Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n))))

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())

P \mapsto \left\{P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\right) \textrm{ if } \forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\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: 17 body: 2
1	ExprTuple	17
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	ExprRange	lambda_map: 11 start_index: 27 end_index: 28
10	Lambda	parameter: 21 body: 12
11	Lambda	parameter: 32 body: 13
12	Conditional	value: 14 condition: 15
13	Operation	operator: 17 operand: 29
14	Operation	operator: 17 operand: 21
15	Operation	operator: 19 operands: 20
16	ExprTuple	29
17	Variable
18	ExprTuple	21
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25
25	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
26	Lambda	parameter: 32 body: 29
27	Literal
28	Variable
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable