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 C, Conditional, ExprTuple, Lambda, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_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, D_1_to_n], instance_expr = And(A_1_to_l, C, B_1_to_m, D_1_to_n), condition = And(A_1_to_l, B_1_to_m, C, D_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, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m}, C,D_{1}, D_{2}, \ldots, D_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land C\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land D_{1} \land  D_{2} \land  \ldots \land  D_{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	29, 31, 34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 23 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	29, 20
15	ExprTuple	31, 20
16	Literal
17	ExprTuple	34, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 26, 25, 27
22	Literal
23	ExprTuple	24, 25, 26, 27
24	ExprRange	lambda_map: 28 start_index: 33 end_index: 29
25	ExprRange	lambda_map: 30 start_index: 33 end_index: 31
26	Variable
27	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
28	Lambda	parameter: 42 body: 35
29	Variable
30	Lambda	parameter: 42 body: 36
31	Variable
32	Lambda	parameter: 42 body: 37
33	Literal
34	Variable
35	IndexedVar	variable: 38 index: 42
36	IndexedVar	variable: 39 index: 42
37	IndexedVar	variable: 40 index: 42
38	Variable
39	Variable
40	Variable
41	ExprTuple	42
42	Variable