Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.universality

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.booleans.quantification import general_bundled_forall_Pxy_if_Qx, general_nested_forall_Pxy_if_Qx

# build up the expression from sub-expressions
expr = ExprTuple(general_nested_forall_Pxy_if_Qx, general_bundled_forall_Pxy_if_Qx)

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