Expression of type Lambda

from the theory of proveit.logic.sets.intersection

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, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, InSet, Intersect
from proveit.logic.sets import x_in_every_A
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = InSet(x, Intersect(A_1_to_m)), condition = x_in_every_A), InSet(m, NaturalPos)))

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_{x, A_{1}, A_{2}, \ldots, A_{m}~|~\left(x \in A_{1}\right), \left(x \in A_{2}\right), \ldots, \left(x \in A_{m}\right)}~\left(x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)\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: 26 body: 2
1	ExprTuple	26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 27 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	26, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	29, 22
11	Conditional	value: 12 condition: 13
12	Operation	operator: 27 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	29, 17
15	Literal
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	ExprRange	lambda_map: 21 start_index: 25 end_index: 26
19	Literal
20	ExprTuple	22
21	Lambda	parameter: 33 body: 23
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Operation	operator: 27 operands: 28
24	Lambda	parameter: 33 body: 30
25	Literal
26	Variable
27	Literal
28	ExprTuple	29, 30
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable