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Expression of type Conditional

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, 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 = 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())
\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()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 22
operands: 5
3Literal
4ExprTuple6
5ExprTuple26, 7
6Lambdaparameters: 8
body: 9
7Literal
8ExprTuple27, 21
9Conditionalvalue: 10
condition: 11
10Operationoperator: 12
operands: 13
11Operationoperator: 22
operands: 14
12Literal
13ExprTuple15
14ExprTuple27, 16
15ExprRangelambda_map: 17
start_index: 25
end_index: 26
16Operationoperator: 18
operands: 19
17Lambdaparameter: 31
body: 20
18Literal
19ExprTuple21
20Operationoperator: 22
operands: 23
21ExprRangelambda_map: 24
start_index: 25
end_index: 26
22Literal
23ExprTuple27, 28
24Lambdaparameter: 31
body: 28
25Literal
26Variable
27Variable
28IndexedVarvariable: 29
index: 31
29Variable
30ExprTuple31
31Variable