Expression of type Forall

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

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

\forall_{P~|~P\left(\top\right) = \top, P\left(\bot\right) = \top}~\left(\left[\forall_{A \in \mathbb{B}}~P\left(A\right)\right] = \top\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 13 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 28 body: 4
3	ExprTuple	28
4	Conditional	value: 5 condition: 6
5	Operation	operator: 16 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 26
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operand: 18
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Literal
14	ExprTuple	18
15	ExprTuple	19, 26
16	Literal
17	ExprTuple	20, 26
18	Lambda	parameter: 32 body: 21
19	Operation	operator: 28 operand: 26
20	Operation	operator: 28 operand: 27
21	Conditional	value: 24 condition: 25
22	ExprTuple	26
23	ExprTuple	27
24	Operation	operator: 28 operand: 32
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	Variable
29	ExprTuple	32
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Literal