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_n, Q__x_1_to_n, R__x_1_to_n
from proveit.logic import Implies

# build up the expression from sub-expressions
expr = Conditional(Implies(P__x_1_to_n, R__x_1_to_n), Q__x_1_to_n)

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\{P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow R\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } Q\left(x_{1}, x_{2}, \ldots, x_{n}\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 operands: 4
2	Operation	operator: 5 operands: 10
3	Literal
4	ExprTuple	6, 7
5	Variable
6	Operation	operator: 8 operands: 10
7	Operation	operator: 9 operands: 10
8	Variable
9	Variable
10	ExprTuple	11
11	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
12	Lambda	parameter: 18 body: 15
13	Literal
14	Variable
15	IndexedVar	variable: 16 index: 18
16	Variable
17	ExprTuple	18
18	Variable