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 Conditional, Lambda, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Equals, Forall, InSet, TRUE
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = Equals(And(A_1_to_m), TRUE), condition = A_1_to_m), 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_{1}, A_{2}, \ldots, A_{m}~|~A_{1}, A_{2}, \ldots, A_{m}}~\left(\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m}\right) = \top\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: 22 body: 2
1	ExprTuple	22
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	22, 10
9	Lambda	parameters: 18 body: 11
10	Literal
11	Conditional	value: 12 condition: 15
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Literal
17	Literal
18	ExprTuple	19
19	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
20	Lambda	parameter: 26 body: 23
21	Literal
22	Variable
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable