# from the theory of proveit.logic.sets.unification¶

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.
# 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, Union
from proveit.logic.sets import x_in_any_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 = InSet(x, Union(A_1_to_m)), condition = x_in_any_A), 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}~|~\left(x \in A_{1}\right) \lor  \left(x \in A_{2}\right) \lor  \ldots \lor  \left(x \in A_{m}\right)}~\left(x \in \left(A_{1} \cup  A_{2} \cup  \ldots \cup  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: 26
body: 2
1ExprTuple26
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 27
operands: 7
5Literal
6ExprTuple8
7ExprTuple26, 9
8Lambdaparameters: 10
body: 11
9Literal
10ExprTuple29, 22
11Conditionalvalue: 12
condition: 13
12Operationoperator: 27
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple29, 17
15Literal
16ExprTuple18
17Operationoperator: 19
operands: 20
18ExprRangelambda_map: 21
start_index: 25
end_index: 26
19Literal
20ExprTuple22
21Lambdaparameter: 33
body: 23
22ExprRangelambda_map: 24
start_index: 25
end_index: 26
23Operationoperator: 27
operands: 28
24Lambdaparameter: 33
body: 30
25Literal
26Variable
27Literal
28ExprTuple29, 30
29Variable
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable