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 B, Conditional, ExprTuple, Lambda, m, n
from proveit.core_expr_types import A_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
sub_expr1 = [A_1_to_m, B, C_1_to_n]
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = B, conditions = sub_expr1), And(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(m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{m}, B,C_{1}, C_{2}, \ldots, C_{n}}~B \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	24, 27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 18 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 19 body: 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Conditional	value: 21 condition: 16
13	ExprTuple	24, 17
14	Literal
15	ExprTuple	27, 17
16	Operation	operator: 18 operands: 19
17	Literal
18	Literal
19	ExprTuple	20, 21, 22
20	ExprRange	lambda_map: 23 start_index: 26 end_index: 24
21	Variable
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Lambda	parameter: 33 body: 28
24	Variable
25	Lambda	parameter: 33 body: 29
26	Literal
27	Variable
28	IndexedVar	variable: 30 index: 33
29	IndexedVar	variable: 31 index: 33
30	Variable
31	Variable
32	ExprTuple	33
33	Variable