Theorem forall_over_bool_by_cases 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 forall_over_bool_by_cases

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

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