Expression of type Lambda

from the theory of proveit.logic.booleans.conjunction

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 A, Conditional, ExprRange, Lambda, Variable, n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [A], instance_expr = And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, one, n)), condition = A), 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~|~A}~\left(A \land  A \land  ..\left(n - 3\right) \times.. \land  A\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: 19 body: 2
1	ExprTuple	19
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	19, 10
9	Lambda	parameter: 21 body: 12
10	Literal
11	ExprTuple	21
12	Conditional	value: 13 condition: 21
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16
16	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
17	Lambda	parameter: 22 body: 21
18	Literal
19	Variable
20	ExprTuple	22
21	Variable
22	Variable