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 Conditional, ExprTuple, Lambda, P, Q
from proveit.logic import 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], Conditional(general_exists_Px_st_Qx, Not(general_forall__Py_not_T__st_Qy))))

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\{\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) \textrm{ if } \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]\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	31, 26
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operand: 11
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Lambda	parameters: 18 body: 12
11	Operation	operator: 13 operand: 17
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 31 operands: 18
16	Operation	operator: 26 operands: 18
17	Lambda	parameters: 32 body: 19
18	ExprTuple	20
19	Conditional	value: 21 condition: 22
20	ExprRange	lambda_map: 23 start_index: 35 end_index: 36
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 32
23	Lambda	parameter: 40 body: 27
24	Literal
25	ExprTuple	28, 29
26	Variable
27	IndexedVar	variable: 30 index: 40
28	Operation	operator: 31 operands: 32
29	Literal
30	Variable
31	Variable
32	ExprTuple	33
33	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
34	Lambda	parameter: 40 body: 37
35	Literal
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable