Expression of type ExprTuple

from the theory of proveit.logic.booleans.disjunction

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 A, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, InSet, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = Not(Or(A_1_to_m)), condition = ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m)), InSet(m, 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(m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}~|~(\lnot A_{1}), (\lnot A_{2}), \ldots, (\lnot A_{m})}~(\lnot \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right)) \textrm{ if } m \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	parameter: 27 body: 3
2	ExprTuple	27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	27, 11
10	Lambda	parameters: 21 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 28 operand: 18
14	Operation	operator: 16 operands: 17
15	ExprTuple	18
16	Literal
17	ExprTuple	19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 33 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operand: 30
25	Lambda	parameter: 33 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable