Expression of type Forall

from the theory of proveit.logic.booleans.conjunction

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 C
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_1_to_n
from proveit.logic import And, Boolean, Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C, D_1_to_n], instance_expr = Equals(And(A_1_to_l, B_1_to_m, C, D_1_to_n), And(A_1_to_l, C, B_1_to_m, D_1_to_n)).with_wrapping_at(2), domain = Boolean)

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_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C, D_{1}, D_{2}, \ldots, D_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m} \land C\land D_{1} \land  D_{2} \land  \ldots \land  D_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land C\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land D_{1} \land  D_{2} \land  \ldots \land  D_{n}\right) \end{array} \end{array}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 16 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 17 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	12, 13, 14, 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	ExprRange	lambda_map: 19 start_index: 35 end_index: 31
13	ExprRange	lambda_map: 20 start_index: 35 end_index: 33
14	Operation	operator: 39 operands: 21
15	ExprRange	lambda_map: 22 start_index: 35 end_index: 36
16	ExprTuple	23, 24, 28, 25
17	Literal
18	ExprTuple	23, 28, 24, 25
19	Lambda	parameter: 49 body: 26
20	Lambda	parameter: 49 body: 27
21	ExprTuple	28, 44
22	Lambda	parameter: 49 body: 29
23	ExprRange	lambda_map: 30 start_index: 35 end_index: 31
24	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
25	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
26	Operation	operator: 39 operands: 37
27	Operation	operator: 39 operands: 38
28	Variable
29	Operation	operator: 39 operands: 40
30	Lambda	parameter: 49 body: 41
31	Variable
32	Lambda	parameter: 49 body: 42
33	Variable
34	Lambda	parameter: 49 body: 43
35	Literal
36	Variable
37	ExprTuple	41, 44
38	ExprTuple	42, 44
39	Literal
40	ExprTuple	43, 44
41	IndexedVar	variable: 45 index: 49
42	IndexedVar	variable: 46 index: 49
43	IndexedVar	variable: 47 index: 49
44	Literal
45	Variable
46	Variable
47	Variable
48	ExprTuple	49
49	Variable