Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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, B, C
from proveit.logic import Boolean, Forall, Implies, Or

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = Forall(instance_param_or_params = [C], instance_expr = C, conditions = [Implies(A, C), Implies(B, C)]), domain = Boolean, condition = Or(A, B))

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_{A, B \in \mathbb{B}~|~A \lor B}~\left[\forall_{C~|~A \Rightarrow C, B \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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 19 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameter: 31 body: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	31
14	Conditional	value: 31 condition: 20
15	ExprTuple	29, 21
16	Literal
17	ExprTuple	30, 21
18	Literal
19	ExprTuple	29, 30
20	Operation	operator: 22 operands: 23
21	Literal
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 31
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable