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, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_1_to_n
from proveit.logic import And, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l, m, n], instance_expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C, D_1_to_n], instance_expr = And(A_1_to_l, C, B_1_to_m, D_1_to_n), condition = And(A_1_to_l, B_1_to_m, C, D_1_to_n)), 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_{l, m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m}, C,D_{1}, D_{2}, \ldots, D_{n}}~\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)\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, 32, 35
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 23 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 24 body: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Conditional	value: 19 condition: 20
15	ExprTuple	30, 21
16	ExprTuple	32, 21
17	Literal
18	ExprTuple	35, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 27, 26, 28
23	Literal
24	ExprTuple	25, 26, 27, 28
25	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
26	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
27	Variable
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Lambda	parameter: 43 body: 36
30	Variable
31	Lambda	parameter: 43 body: 37
32	Variable
33	Lambda	parameter: 43 body: 38
34	Literal
35	Variable
36	IndexedVar	variable: 39 index: 43
37	IndexedVar	variable: 40 index: 43
38	IndexedVar	variable: 41 index: 43
39	Variable
40	Variable
41	Variable
42	ExprTuple	43
43	Variable