Expression of type Conditional

from the theory of proveit.logic.booleans

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 A, B, Conditional, Function, P
from proveit.logic import Boolean, Forall, InSet

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [B], instance_expr = Function(P, [A, B]), domain = Boolean), InSet(A, Boolean))

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_{B \in \mathbb{B}}~P\left(A, B\right) \textrm{ if } A \in \mathbb{B}\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: 13 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	15, 17
6	Lambda	parameter: 16 body: 8
7	ExprTuple	16
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Variable
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	16, 17
15	Variable
16	Variable
17	Literal