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, Conditional, PofA, QofA
from proveit.logic import And, Boolean, Forall, QimplPofFalse, QimplPofTrue

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean, condition = QofA), And(QimplPofTrue, QimplPofFalse))

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 \in \mathbb{B}~|~Q\left(A\right)}~P\left(A\right) \textrm{ if } Q\left(\top\right) \Rightarrow P\left(\top\right) ,  Q\left(\bot\right) \Rightarrow P\left(\bot\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: 6
2	Operation	operator: 19 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 33 body: 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Conditional	value: 13 condition: 14
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	17, 18
13	Operation	operator: 22 operand: 33
14	Operation	operator: 19 operands: 20
15	Operation	operator: 30 operand: 26
16	Operation	operator: 22 operand: 26
17	Operation	operator: 30 operand: 27
18	Operation	operator: 22 operand: 27
19	Literal
20	ExprTuple	24, 25
21	ExprTuple	26
22	Variable
23	ExprTuple	27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operand: 33
26	Literal
27	Literal
28	Literal
29	ExprTuple	33, 32
30	Variable
31	ExprTuple	33
32	Literal
33	Variable