Expression of type ExprTuple

from the theory of proveit.core_expr_types.conditionals

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, a, m
from proveit.core_expr_types import Q_1_to_m
from proveit.logic import And, Equals, Forall, InSet, TRUE
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = And(Q_1_to_m)
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [a, Q_1_to_m], instance_expr = Equals(Conditional(a, And(TRUE, sub_expr1)), Conditional(a, sub_expr1)).with_wrapping_at(1)), 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, Q_{1}, Q_{2}, \ldots, Q_{m}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } \top ,  Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m}\right.. \\  = \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m}\right.. \end{array} \end{array}\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: 28 body: 3
2	ExprTuple	28
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	28, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	19, 25
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Conditional	value: 19 condition: 18
17	Conditional	value: 19 condition: 22
18	Operation	operator: 23 operands: 20
19	Variable
20	ExprTuple	21, 22
21	Literal
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25
25	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
26	Lambda	parameter: 32 body: 29
27	Literal
28	Variable
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable