Expression of type ExprTuple

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 ExprTuple, 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 = ExprTuple(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(\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)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	32, 35, 34
3	Operation	operator: 21 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 21 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 31 body: 13
11	Operation	operator: 15 operand: 19
12	Operation	operator: 15 operand: 20
13	Conditional	value: 17 condition: 18
14	ExprTuple	19
15	Literal
16	ExprTuple	20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 35 operands: 31
19	Lambda	parameters: 33 body: 23
20	Lambda	parameters: 36 body: 24
21	Literal
22	ExprTuple	25, 26
23	Conditional	value: 27 condition: 28
24	Conditional	value: 29 condition: 30
25	Operation	operator: 32 operands: 31
26	Operation	operator: 34 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 35 operands: 33
29	Operation	operator: 34 operands: 36
30	Operation	operator: 35 operands: 36
31	ExprTuple	37
32	Variable
33	ExprTuple	38
34	Variable
35	Variable
36	ExprTuple	39
37	ExprRange	lambda_map: 40 start_index: 43 end_index: 44
38	ExprRange	lambda_map: 41 start_index: 43 end_index: 44
39	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
40	Lambda	parameter: 52 body: 45
41	Lambda	parameter: 52 body: 46
42	Lambda	parameter: 52 body: 47
43	Literal
44	Variable
45	IndexedVar	variable: 48 index: 52
46	IndexedVar	variable: 49 index: 52
47	IndexedVar	variable: 50 index: 52
48	Variable
49	Variable
50	Variable
51	ExprTuple	52
52	Variable