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
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(general_forall_st_Qx__Px_implies_Rx, Implies(general_exists_Py_st_Qy, general_exists_Rz_st_Qz).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(\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), \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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