Expression of type Lambda

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 Conditional, ExprRange, IndexedVar, Lambda, 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, InSet
from proveit.numbers import NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(i, Conditional(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)), InSet(i, NaturalPos)))

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())

i \mapsto \left\{\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) \textrm{ if } i \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 27 body: 2
1	ExprTuple	27
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	27, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	21, 22
12	Conditional	value: 13 condition: 14
13	Operation	operator: 29 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	ExprTuple	21
19	ExprTuple	22
20	ExprRange	lambda_map: 23 start_index: 26 end_index: 27
21	ExprRange	lambda_map: 24 start_index: 26 end_index: 27
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Lambda	parameter: 36 body: 28
24	Lambda	parameter: 36 body: 31
25	Lambda	parameter: 36 body: 32
26	Literal
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	IndexedVar	variable: 33 index: 36
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable