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
from proveit.logic import And, Boolean, Equals, Forall, PofFalse, PofTrue, TRUE

# build up the expression from sub-expressions
expr = Conditional(Equals(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean), TRUE), And(Equals(PofTrue, TRUE), Equals(PofFalse, TRUE)))

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