Expression of type Conditional

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

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, Q_1_to_m, R], instance_expr = Equals(Conditional(a, And(And(Q_1_to_m), R)), Conditional(a, And(Q_1_to_m, R))).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\{\forall_{a, Q_{1}, Q_{2}, \ldots, Q_{m}, R}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m} ,  R\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m} ,  R\right.. \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	27, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	16, 24, 21
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Conditional	value: 16 condition: 15
14	Conditional	value: 16 condition: 17
15	Operation	operator: 22 operands: 18
16	Variable
17	Operation	operator: 22 operands: 19
18	ExprTuple	20, 21
19	ExprTuple	24, 21
20	Operation	operator: 22 operands: 23
21	Variable
22	Literal
23	ExprTuple	24
24	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
25	Lambda	parameter: 31 body: 28
26	Literal
27	Variable
28	IndexedVar	variable: 29 index: 31
29	Variable
30	ExprTuple	31
31	Variable