Expression of type ExprTuple

from the theory of proveit.logic.booleans.conjunction

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, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = And(A_1_to_l, B_1_to_m, C_1_to_n), condition = And(A_1_to_l, And(B_1_to_m), C_1_to_n)), And(InSet(l, Natural), InSet(m, Natural), InSet(n, Natural)))))

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(l, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l}, B_{1} \land  B_{2} \land  \ldots \land  B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \textrm{ if } l \in \mathbb{N} ,  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	27, 38, 31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 28 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 21 body: 13
10	Operation	operator: 16 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Conditional	value: 18 condition: 19
14	ExprTuple	27, 20
15	ExprTuple	38, 20
16	Literal
17	ExprTuple	31, 20
18	Operation	operator: 28 operands: 21
19	Operation	operator: 28 operands: 22
20	Literal
21	ExprTuple	23, 33, 25
22	ExprTuple	23, 24, 25
23	ExprRange	lambda_map: 26 start_index: 37 end_index: 27
24	Operation	operator: 28 operands: 29
25	ExprRange	lambda_map: 30 start_index: 37 end_index: 31
26	Lambda	parameter: 43 body: 32
27	Variable
28	Literal
29	ExprTuple	33
30	Lambda	parameter: 43 body: 34
31	Variable
32	IndexedVar	variable: 35 index: 43
33	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
34	IndexedVar	variable: 39 index: 43
35	Variable
36	Lambda	parameter: 43 body: 40
37	Literal
38	Variable
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable