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 Conditional, ExprTuple, Lambda, P, Q, R, m, n
from proveit.logic import And, Forall, Implies, InSet
from proveit.logic.booleans.quantification import general_bundled_forall_Pxy_if_Qx, general_nested_forall_Pxy_if_Qx
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [P, Q, R], instance_expr = Implies(general_nested_forall_Pxy_if_Qx, general_bundled_forall_Pxy_if_Qx).with_wrapping_at(1)), And(InSet(m, NaturalPos), InSet(n, NaturalPos)))))

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(m, n\right) \mapsto \left\{\forall_{P, Q, R}~\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) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\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	47, 50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 29 operand: 8
5	Operation	operator: 31 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	41, 37, 42
12	Operation	operator: 16 operands: 17
13	ExprTuple	47, 18
14	Literal
15	ExprTuple	50, 18
16	Literal
17	ExprTuple	19, 20
18	Literal
19	Operation	operator: 29 operand: 23
20	Operation	operator: 29 operand: 24
21	ExprTuple	23
22	ExprTuple	24
23	Lambda	parameters: 38 body: 25
24	Lambda	parameters: 43 body: 26
25	Conditional	value: 27 condition: 34
26	Conditional	value: 39 condition: 28
27	Operation	operator: 29 operand: 33
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34, 40
33	Lambda	parameters: 35 body: 36
34	Operation	operator: 37 operands: 38
35	ExprTuple	45
36	Conditional	value: 39 condition: 40
37	Variable
38	ExprTuple	44
39	Operation	operator: 41 operands: 43
40	Operation	operator: 42 operands: 43
41	Variable
42	Variable
43	ExprTuple	44, 45
44	ExprRange	lambda_map: 46 start_index: 49 end_index: 47
45	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
46	Lambda	parameter: 56 body: 51
47	Variable
48	Lambda	parameter: 56 body: 52
49	Literal
50	Variable
51	IndexedVar	variable: 53 index: 56
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable