Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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, b, d, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n, d], instance_expr = Equals(Set(a_1_to_m, b, c_1_to_n), Set(a_1_to_m, d, c_1_to_n)).with_wrapping_at(2), condition = Equals(b, d)), And(InSet(m, Natural), InSet(n, 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())

\left(m, n\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}, d~|~b = d}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{m}, d,c_{1}, c_{2}, \ldots, c_{n}\right\} \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N} ,  n \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	parameters: 1 body: 2
1	ExprTuple	33, 36
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	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	29, 28, 31, 30
13	Conditional	value: 17 condition: 18
14	ExprTuple	33, 19
15	Literal
16	ExprTuple	36, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	28, 30
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	29, 28, 31
26	Literal
27	ExprTuple	29, 30, 31
28	Variable
29	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
30	Variable
31	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
32	Lambda	parameter: 42 body: 37
33	Variable
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