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Expression of type Lambda

from the theory of proveit.logic.sets.intersection

In [1]:
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
In [2]:
# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = x_in_every_A, condition = InSet(x, Intersect(A_1_to_m))), InSet(m, NaturalPos)))
expr:
In [3]:
# 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
In [4]:
# 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}~|~x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)}~\left(\left(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right)\right) \textrm{ if } m \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 28
body: 2
1ExprTuple28
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 24
operands: 7
5Literal
6ExprTuple8
7ExprTuple28, 9
8Lambdaparameters: 10
body: 11
9Literal
10ExprTuple29, 23
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 15
13Operationoperator: 24
operands: 16
14Literal
15ExprTuple17
16ExprTuple29, 18
17ExprRangelambda_map: 19
start_index: 27
end_index: 28
18Operationoperator: 20
operands: 21
19Lambdaparameter: 33
body: 22
20Literal
21ExprTuple23
22Operationoperator: 24
operands: 25
23ExprRangelambda_map: 26
start_index: 27
end_index: 28
24Literal
25ExprTuple29, 30
26Lambdaparameter: 33
body: 30
27Literal
28Variable
29Variable
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable