Expression of type Lambda

from the theory of proveit.numbers.ordering

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, S, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet, SubsetEq
from proveit.numbers import Min, Natural, Real

# build up the expression from sub-expressions
expr = Lambda(S, Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Min(a_1_to_n), S), domain = S), domain = Natural), SubsetEq(S, Real)))

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())

S \mapsto \left\{\forall_{n \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{n} \in S}~\left({\rm Min}\left(a_{1}, a_{2}, \ldots, a_{n}\right) \in S\right)\right] \textrm{ if } S \subseteq \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 38 body: 2
1	ExprTuple	38
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	38, 9
8	Lambda	parameter: 34 body: 11
9	Literal
10	ExprTuple	34
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 35 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	34, 18
17	Lambda	parameters: 28 body: 19
18	Literal
19	Conditional	value: 20 condition: 21
20	Operation	operator: 35 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 38
23	Literal
24	ExprTuple	26
25	Operation	operator: 27 operands: 28
26	ExprRange	lambda_map: 29 start_index: 33 end_index: 34
27	Literal
28	ExprTuple	30
29	Lambda	parameter: 41 body: 31
30	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
31	Operation	operator: 35 operands: 36
32	Lambda	parameter: 41 body: 37
33	Literal
34	Variable
35	Literal
36	ExprTuple	37, 38
37	IndexedVar	variable: 39 index: 41
38	Variable
39	Variable
40	ExprTuple	41
41	Variable