Expression of type Conditional

from the theory of proveit.logic.booleans.quantification

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
from proveit.core_expr_types import P__x_1_to_m_y_1_to_n, Q__x_1_to_m, R__x_1_to_m_y_1_to_n, y_1_to_n
from proveit.logic import Forall

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [y_1_to_n], instance_expr = P__x_1_to_m_y_1_to_n, condition = R__x_1_to_m_y_1_to_n), Q__x_1_to_m)

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_{y_{1}, y_{2}, \ldots, y_{n}~|~R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } Q\left(x_{1}, x_{2}, \ldots, x_{m}\right)\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	Variable
6	ExprTuple	15
7	Lambda	parameters: 8 body: 9
8	ExprTuple	16
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 14
11	Operation	operator: 13 operands: 14
12	Variable
13	Variable
14	ExprTuple	15, 16
15	ExprRange	lambda_map: 17 start_index: 20 end_index: 18
16	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
17	Lambda	parameter: 27 body: 22
18	Variable
19	Lambda	parameter: 27 body: 23
20	Literal
21	Variable
22	IndexedVar	variable: 24 index: 27
23	IndexedVar	variable: 25 index: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable