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 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 = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = InSet(x, Union(A_1_to_m)), condition = x_in_any_A), domain = 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())

\forall_{m \in \mathbb{N}^+}~\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)\right]

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 28
body: 4
3ExprTuple28
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 29
operands: 9
7Literal
8ExprTuple10
9ExprTuple28, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple31, 24
13Conditionalvalue: 14
condition: 15
14Operationoperator: 29
operands: 16
15Operationoperator: 17
operands: 18
16ExprTuple31, 19
17Literal
18ExprTuple20
19Operationoperator: 21
operands: 22
20ExprRangelambda_map: 23
start_index: 27
end_index: 28
21Literal
22ExprTuple24
23Lambdaparameter: 35
body: 25
24ExprRangelambda_map: 26
start_index: 27
end_index: 28
25Operationoperator: 29
operands: 30
26Lambdaparameter: 35
body: 32
27Literal
28Variable
29Literal
30ExprTuple31, 32
31Variable
32IndexedVarvariable: 33
index: 35
33Variable
34ExprTuple35
35Variable