Theorem unfold_forall_over_bool of type Forall

from the theory of proveit.logic.booleans

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.booleans import unfold_forall_over_bool

# check that the built expression is the same as the stored expression
assert unfold_forall_over_bool.expr == stored_expr
assert unfold_forall_over_bool.expr._style_id == stored_expr._style_id
print("Passed sanity check: unfold_forall_over_bool matches stored_expr")

Passed sanity check: unfold_forall_over_bool matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

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