Expression of type Forall

from the theory of proveit.core_expr_types.conditionals

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 Conditional, Q, a, n
from proveit.core_expr_types import R_1_to_n
from proveit.logic import And, Equals, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a, Q, R_1_to_n], instance_expr = Equals(Conditional(a, And(Q, And(R_1_to_n))), Conditional(a, And(Q, R_1_to_n))).with_wrapping_at(1)), 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_{n \in \mathbb{N}}~\left[\forall_{a, Q, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\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	parameter: 31 body: 4
3	ExprTuple	31
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	31, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	20, 25, 28
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Conditional	value: 20 condition: 19
18	Conditional	value: 20 condition: 21
19	Operation	operator: 26 operands: 22
20	Variable
21	Operation	operator: 26 operands: 23
22	ExprTuple	25, 24
23	ExprTuple	25, 28
24	Operation	operator: 26 operands: 27
25	Variable
26	Literal
27	ExprTuple	28
28	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable