Expression of type Lambda

from the theory of proveit.core_expr_types.conditionals

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, Q, a, n
from proveit.core_expr_types import R_1_to_n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a, Q, R_1_to_n], instance_expr = Equals(Conditional(a, And(Q, And(R_1_to_n))), Conditional(a, And(Q, R_1_to_n))).with_wrapping_at(1)), 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())

n \mapsto \left\{\forall_{a, Q, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\right) \textrm{ if } 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	parameter: 29 body: 2
1	ExprTuple	29
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	29, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	18, 23, 26
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Conditional	value: 18 condition: 17
16	Conditional	value: 18 condition: 19
17	Operation	operator: 24 operands: 20
18	Variable
19	Operation	operator: 24 operands: 21
20	ExprTuple	23, 22
21	ExprTuple	23, 26
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26
26	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
27	Lambda	parameter: 33 body: 30
28	Literal
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable