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, Not
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, B, C_1_to_n], instance_expr = Not(And(A_1_to_m, B, C_1_to_n)), condition = Not(B)), 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}~|~\lnot B}~(\lnot \left(A_{1} \land  A_{2} \land  \ldots \land  A_{m} \land B\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\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	29, 32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 23 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 24 body: 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	29, 18
14	Literal
15	ExprTuple	32, 18
16	Operation	operator: 20 operand: 22
17	Operation	operator: 20 operand: 26
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	26
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26, 27
25	ExprRange	lambda_map: 28 start_index: 31 end_index: 29
26	Variable
27	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
28	Lambda	parameter: 38 body: 33
29	Variable
30	Lambda	parameter: 38 body: 34
31	Literal
32	Variable
33	IndexedVar	variable: 35 index: 38
34	IndexedVar	variable: 36 index: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable