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Expression of type Conditional

from the theory of proveit.numbers.ordering

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, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Min, NaturalPos, Real
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_m, b], instance_expr = Equals(Min(a_1_to_m, b), Min(Min(a_1_to_m), b)), domain = Real), 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_{a_{1}, a_{2}, \ldots, a_{m}, b \in \mathbb{R}}~\left({\rm Min}\left(a_{1}, a_{2}, \ldots, a_{m}, b\right) = {\rm Min}\left({\rm Min}\left(a_{1}, a_{2}, \ldots, a_{m}\right), b\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: 28
operands: 5
3Literal
4ExprTuple6
5ExprTuple34, 7
6Lambdaparameters: 19
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple17, 18
15Operationoperator: 26
operands: 19
16Operationoperator: 26
operands: 20
17ExprRangelambda_map: 21
start_index: 33
end_index: 34
18Operationoperator: 28
operands: 22
19ExprTuple30, 25
20ExprTuple23, 25
21Lambdaparameter: 38
body: 24
22ExprTuple25, 31
23Operationoperator: 26
operands: 27
24Operationoperator: 28
operands: 29
25Variable
26Literal
27ExprTuple30
28Literal
29ExprTuple35, 31
30ExprRangelambda_map: 32
start_index: 33
end_index: 34
31Literal
32Lambdaparameter: 38
body: 35
33Literal
34Variable
35IndexedVarvariable: 36
index: 38
36Variable
37ExprTuple38
38Variable