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 B, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Forall, InSet
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, B, C_1_to_n], instance_expr = InSet(B, Boolean), condition = InSet(And(A_1_to_m, B, C_1_to_n), 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}, B, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m} \land B\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \in \mathbb{B}}~\left(B \in \mathbb{B}\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	30, 33
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 24 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 25 body: 13
11	Operation	operator: 20 operands: 14
12	Operation	operator: 20 operands: 15
13	Conditional	value: 16 condition: 17
14	ExprTuple	30, 18
15	ExprTuple	33, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	27, 23
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27, 28
26	ExprRange	lambda_map: 29 start_index: 32 end_index: 30
27	Variable
28	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
29	Lambda	parameter: 39 body: 34
30	Variable
31	Lambda	parameter: 39 body: 35
32	Literal
33	Variable
34	IndexedVar	variable: 36 index: 39
35	IndexedVar	variable: 37 index: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable