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, a, m
from proveit.core_expr_types import Q_1_to_m
from proveit.logic import And, Equals, Forall, InSet, TRUE
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = And(Q_1_to_m)
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [a, Q_1_to_m], instance_expr = Equals(Conditional(a, And(TRUE, sub_expr1)), Conditional(a, sub_expr1)).with_wrapping_at(1)), InSet(m, 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())

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