Expression of type Lambda

from the theory of proveit.logic.sets.cartesian_products

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, Lambda, m, x
from proveit.core_expr_types import A_1_to_m, a_1_to_m
from proveit.logic import And, CartProd, Equals, Forall, InSet
from proveit.logic.sets.cartesian_products import a_in_A__1_to_m
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m, a_1_to_m], instance_expr = Equals(InSet(x, CartProd(A_1_to_m)), And(Equals(x, [a_1_to_m]), a_in_A__1_to_m)).with_wrapping_at(2)), InSet(m, 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())

m \mapsto \left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}, a_{1}, a_{2}, \ldots, a_{m}}~\left(\begin{array}{c} \begin{array}{l} \left(x \in \left(A_{1} \times  A_{2} \times  \ldots \times  A_{m}\right)\right) =  \\ \left(\left(x = \left(a_{1}, a_{2}, \ldots, a_{m}\right)\right)\land \left(a_{1} \in A_{1}\right) \land  \left(a_{2} \in A_{2}\right) \land  \ldots \land  \left(a_{m} \in A_{m}\right)\right) \end{array} \end{array}\right) \textrm{ if } m \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: 36 body: 2
1	ExprTuple	36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 32 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	36, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	27, 26, 31
11	Operation	operator: 23 operands: 12
12	ExprTuple	13, 14
13	Operation	operator: 32 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	27, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprRange	lambda_map: 25 start_index: 35 end_index: 36
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	Lambda	parameter: 42 body: 29
26	ExprRange	lambda_map: 30 start_index: 35 end_index: 36
27	Variable
28	ExprTuple	31
29	Operation	operator: 32 operands: 33
30	Lambda	parameter: 42 body: 37
31	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
32	Literal
33	ExprTuple	38, 37
34	Lambda	parameter: 42 body: 38
35	Literal
36	Variable
37	IndexedVar	variable: 39 index: 42
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable