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, C
from proveit.logic import Boolean, Forall, Implies, Not

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [C], instance_expr = Forall(instance_param_or_params = [A], instance_expr = C, domain = Boolean, conditions = [Implies(A, C), Implies(Not(A), C)]))

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