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 A, B, Conditional, Lambda, P, Q
from proveit.logic import Implies, SubsetEq
from proveit.logic.booleans.quantification import general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy

# build up the expression from sub-expressions
expr = Lambda([P, Q, A, B], Conditional(Implies(general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy).with_wrapping_at(2), SubsetEq(A, B)))

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, A, B\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left[\exists_{x_{1}, x_{2}, \ldots, x_{n} \in A~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ \left[\exists_{y_{1}, y_{2}, \ldots, y_{n} \in B~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \end{array} \end{array} \textrm{ if } A \subseteq B\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	23, 33, 46, 48
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	46, 48
9	Operation	operator: 12 operand: 14
10	Operation	operator: 12 operand: 15
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	Lambda	parameters: 31 body: 16
15	Lambda	parameters: 34 body: 17
16	Conditional	value: 18 condition: 19
17	Conditional	value: 20 condition: 21
18	Operation	operator: 23 operands: 31
19	Operation	operator: 24 operands: 22
20	Operation	operator: 23 operands: 34
21	Operation	operator: 24 operands: 25
22	ExprTuple	26, 27
23	Variable
24	Literal
25	ExprTuple	28, 29
26	ExprRange	lambda_map: 30 start_index: 44 end_index: 45
27	Operation	operator: 33 operands: 31
28	ExprRange	lambda_map: 32 start_index: 44 end_index: 45
29	Operation	operator: 33 operands: 34
30	Lambda	parameter: 53 body: 35
31	ExprTuple	36
32	Lambda	parameter: 53 body: 37
33	Variable
34	ExprTuple	38
35	Operation	operator: 41 operands: 39
36	ExprRange	lambda_map: 40 start_index: 44 end_index: 45
37	Operation	operator: 41 operands: 42
38	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
39	ExprTuple	47, 46
40	Lambda	parameter: 53 body: 47
41	Literal
42	ExprTuple	49, 48
43	Lambda	parameter: 53 body: 49
44	Literal
45	Variable
46	Variable
47	IndexedVar	variable: 50 index: 53
48	Variable
49	IndexedVar	variable: 51 index: 53
50	Variable
51	Variable
52	ExprTuple	53
53	Variable