Expression of type Lambda

from the theory of proveit.logic.booleans.quantification.existence

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, Q, n
from proveit.core_expr_types import P__y_1_to_n, Q__y_1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [P, Q], instance_expr = Forall(instance_param_or_params = [y_1_to_n], instance_expr = general_exists_Px_st_Qx, conditions = [P__y_1_to_n, Q__y_1_to_n])), InSet(n, NaturalPos)))

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_{P, Q}~\left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right), Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\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: 38 body: 2
1	ExprTuple	38
2	Conditional	value: 3 condition: 4
3	Operation	operator: 12 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	38, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	30, 31
11	Operation	operator: 12 operand: 14
12	Literal
13	ExprTuple	14
14	Lambda	parameters: 26 body: 15
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Lambda	parameters: 32 body: 25
23	Operation	operator: 30 operands: 26
24	Operation	operator: 31 operands: 26
25	Conditional	value: 27 condition: 28
26	ExprTuple	29
27	Operation	operator: 30 operands: 32
28	Operation	operator: 31 operands: 32
29	ExprRange	lambda_map: 33 start_index: 37 end_index: 38
30	Variable
31	Variable
32	ExprTuple	34
33	Lambda	parameter: 43 body: 35
34	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
35	IndexedVar	variable: 39 index: 43
36	Lambda	parameter: 43 body: 40
37	Literal
38	Variable
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable