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_notPx_st_Qx, general_forall_Py_if_Qy

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