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, R
from proveit.logic import Implies
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy, general_exists_Rz_st_Qz, general_forall_st_Qx__Px_implies_Rx

# build up the expression from sub-expressions
expr = Lambda([P, Q, R], Implies(general_forall_st_Qx__Px_implies_Rx, Implies(general_exists_Py_st_Qy, general_exists_Rz_st_Qz).with_wrapping_at(2)).with_wrapping_at(2))

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