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 B, Conditional, Lambda, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [A_1_to_m, B, C_1_to_n]
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = B, conditions = sub_expr1), 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}~|~A_{1}, A_{2}, \ldots, A_{m}, B,C_{1}, C_{2}, \ldots, C_{n}}~B \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	23, 26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 17 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 18 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 20 condition: 15
12	ExprTuple	23, 16
13	Literal
14	ExprTuple	26, 16
15	Operation	operator: 17 operands: 18
16	Literal
17	Literal
18	ExprTuple	19, 20, 21
19	ExprRange	lambda_map: 22 start_index: 25 end_index: 23
20	Variable
21	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
22	Lambda	parameter: 32 body: 27
23	Variable
24	Lambda	parameter: 32 body: 28
25	Literal
26	Variable
27	IndexedVar	variable: 29 index: 32
28	IndexedVar	variable: 30 index: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable