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
from proveit.logic import Implies, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_forall__Py_not_T__st_Qy

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([P, Q], Implies(general_exists_Px_st_Qx, Not(general_forall__Py_not_T__st_Qy)).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\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ (\lnot \left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \neq \top\right)\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	33, 28
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operand: 13
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameters: 20 body: 14
13	Operation	operator: 15 operand: 19
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 33 operands: 20
18	Operation	operator: 28 operands: 20
19	Lambda	parameters: 34 body: 21
20	ExprTuple	22
21	Conditional	value: 23 condition: 24
22	ExprRange	lambda_map: 25 start_index: 37 end_index: 38
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 34
25	Lambda	parameter: 42 body: 29
26	Literal
27	ExprTuple	30, 31
28	Variable
29	IndexedVar	variable: 32 index: 42
30	Operation	operator: 33 operands: 34
31	Literal
32	Variable
33	Variable
34	ExprTuple	35
35	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
36	Lambda	parameter: 42 body: 39
37	Literal
38	Variable
39	IndexedVar	variable: 40 index: 42
40	Variable
41	ExprTuple	42
42	Variable