Theorem conditioned_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 conditioned_forall_over_bool_by_cases

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

Passed sanity check: conditioned_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, Q~|~Q\left(\top\right) \Rightarrow P\left(\top\right), Q\left(\bot\right) \Rightarrow P\left(\bot\right)}~\left[\forall_{A \in \mathbb{B}~|~Q\left(A\right)}~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	parameters: 3 body: 4
3	ExprTuple	26, 34
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 23 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameter: 37 body: 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Conditional	value: 17 condition: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 22
17	Operation	operator: 26 operand: 37
18	Operation	operator: 23 operands: 24
19	Operation	operator: 34 operand: 30
20	Operation	operator: 26 operand: 30
21	Operation	operator: 34 operand: 31
22	Operation	operator: 26 operand: 31
23	Literal
24	ExprTuple	28, 29
25	ExprTuple	30
26	Variable
27	ExprTuple	31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operand: 37
30	Literal
31	Literal
32	Literal
33	ExprTuple	37, 36
34	Variable
35	ExprTuple	37
36	Literal
37	Variable