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, Q, Qx, n, x
from proveit.core_expr_types import Qk_implies_Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [P, Q], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n), condition = Qx), condition = Qk_implies_Pk_a1_to_an)), InSet(n, 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())

n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n}}~\left[\forall_{P, Q~|~\left(Q\left(a_{1}\right) \Rightarrow P\left(a_{1}\right)\right), \left(Q\left(a_{2}\right) \Rightarrow P\left(a_{2}\right)\right), \ldots, \left(Q\left(a_{n}\right) \Rightarrow P\left(a_{n}\right)\right)}~\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}~|~Q\left(x\right)}~P\left(x\right)\right]\right] \textrm{ if } n \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 47 body: 2
1	ExprTuple	47
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 7
4	Operation	operator: 34 operands: 6
5	ExprTuple	7
6	ExprTuple	47, 8
7	Lambda	parameters: 43 body: 9
8	Literal
9	Operation	operator: 16 operand: 11
10	ExprTuple	11
11	Lambda	parameters: 12 body: 13
12	ExprTuple	38, 37
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 26 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20
19	Lambda	parameter: 41 body: 21
20	ExprRange	lambda_map: 22 start_index: 46 end_index: 47
21	Conditional	value: 23 condition: 24
22	Lambda	parameter: 51 body: 25
23	Operation	operator: 38 operand: 41
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 37 operand: 41
32	Operation	operator: 37 operand: 48
33	Operation	operator: 38 operand: 48
34	Literal
35	ExprTuple	41, 40
36	ExprTuple	41
37	Variable
38	Variable
39	ExprTuple	48
40	Operation	operator: 42 operands: 43
41	Variable
42	Literal
43	ExprTuple	44
44	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
45	Lambda	parameter: 51 body: 48
46	Literal
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable