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 Lambda, P, Q, alpha
from proveit.core_expr_types import P__x_1_to_n, Q__x_1_to_n, x_1_to_n
from proveit.logic import And, Forall, Implies
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy

# build up the expression from sub-expressions
expr = Lambda([P, Q, alpha], Implies(And(general_exists_Py_st_Qy, Forall(instance_param_or_params = [x_1_to_n], instance_expr = Implies(P__x_1_to_n, alpha), condition = Q__x_1_to_n)), alpha))

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