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 m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, FALSE, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, n], instance_expr = Forall(instance_param_or_params = [A_1_to_m, C_1_to_n], instance_expr = Equals(And(A_1_to_m, FALSE, C_1_to_n), FALSE), domain = Boolean), domain = Natural)

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