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, a, m, n
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, Forall, InSet, TRUE
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_1_to_n], instance_expr = Equals(Conditional(a, And(Q_1_to_m, TRUE, R_1_to_n)), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1)), 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\{\forall_{a, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m} ,  \top, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N} ,  n \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: 6
2	Operation	operator: 23 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	20, 26, 27
10	Operation	operator: 14 operands: 15
11	ExprTuple	29, 16
12	Literal
13	ExprTuple	32, 16
14	Literal
15	ExprTuple	17, 18
16	Literal
17	Conditional	value: 20 condition: 19
18	Conditional	value: 20 condition: 21
19	Operation	operator: 23 operands: 22
20	Variable
21	Operation	operator: 23 operands: 24
22	ExprTuple	26, 25, 27
23	Literal
24	ExprTuple	26, 27
25	Literal
26	ExprRange	lambda_map: 28 start_index: 31 end_index: 29
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