Expression of type Forall

from the theory of proveit.core_expr_types.expr_arrays

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 ExprRange, IndexedVar, Variable, VertExprArray, a, b, i
from proveit.core_expr_types import a_1_to_i, b_1_to_i
from proveit.logic import Equals, Forall
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_i], instance_expr = Equals(VertExprArray(a_1_to_i), VertExprArray(b_1_to_i)), condition = ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), IndexedVar(b, sub_expr1)), one, i))

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_{i}, b_{1}, b_{2}, \ldots, b_{i}~|~\left(a_{1} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{i} = b_{i}\right)}~\left(\left(\begin{array}{cccc} 
 \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{1} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{2} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{i} \\ \downarrow \end{array}$} \\
\end{array}
\right) = \left(\begin{array}{cccc} 
 \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{1} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{2} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{i} \\ \downarrow \end{array}$} \\
\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	14, 15
5	Conditional	value: 6 condition: 7
6	Operation	operator: 22 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13
11	ExprTuple	14
12	ExprTuple	15
13	ExprRange	lambda_map: 16 start_index: 19 end_index: 20
14	ExprRange	lambda_map: 17 start_index: 19 end_index: 20
15	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
16	Lambda	parameter: 29 body: 21
17	Lambda	parameter: 29 body: 24
18	Lambda	parameter: 29 body: 25
19	Literal
20	Variable
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	IndexedVar	variable: 26 index: 29
25	IndexedVar	variable: 27 index: 29
26	Variable
27	Variable
28	ExprTuple	29
29	Variable