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, Lambda, P, Q, R
from proveit.logic import Implies
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(Lambda([P, Q, R], Implies(general_nested_forall_Pxy_if_Qx, general_bundled_forall_Pxy_if_Qx).with_wrapping_at(1)))

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, R\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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]\right] \\  \Rightarrow \left[\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] \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	28, 24, 29
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 16 operand: 10
7	Operation	operator: 16 operand: 11
8	ExprTuple	10
9	ExprTuple	11
10	Lambda	parameters: 25 body: 12
11	Lambda	parameters: 30 body: 13
12	Conditional	value: 14 condition: 21
13	Conditional	value: 26 condition: 15
14	Operation	operator: 16 operand: 20
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	21, 27
20	Lambda	parameters: 22 body: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	32
23	Conditional	value: 26 condition: 27
24	Variable
25	ExprTuple	31
26	Operation	operator: 28 operands: 30
27	Operation	operator: 29 operands: 30
28	Variable
29	Variable
30	ExprTuple	31, 32
31	ExprRange	lambda_map: 33 start_index: 36 end_index: 34
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Lambda	parameter: 43 body: 38
34	Variable
35	Lambda	parameter: 43 body: 39
36	Literal
37	Variable
38	IndexedVar	variable: 40 index: 43
39	IndexedVar	variable: 41 index: 43
40	Variable
41	Variable
42	ExprTuple	43
43	Variable