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Expression of type Forall

from the theory of proveit.numbers.addition

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 b
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import Forall, InSet
from proveit.numbers import Add, Less, RationalNeg, RationalNonPos, zero
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = InSet(Add(a_1_to_i, b, c_1_to_j), RationalNeg), domain = RationalNonPos, condition = Less(b, zero))
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_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{Q}^{\leq 0}~|~b < 0}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{Q}^-\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 17
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 35
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14, 15
10Operationoperator: 16
operands: 17
11Literal
12ExprRangelambda_map: 18
start_index: 32
end_index: 30
13Operationoperator: 35
operands: 19
14ExprRangelambda_map: 20
start_index: 32
end_index: 33
15Operationoperator: 21
operands: 22
16Literal
17ExprTuple23, 27, 24
18Lambdaparameter: 43
body: 25
19ExprTuple27, 39
20Lambdaparameter: 43
body: 26
21Literal
22ExprTuple27, 28
23ExprRangelambda_map: 29
start_index: 32
end_index: 30
24ExprRangelambda_map: 31
start_index: 32
end_index: 33
25Operationoperator: 35
operands: 34
26Operationoperator: 35
operands: 36
27Variable
28Literal
29Lambdaparameter: 43
body: 37
30Variable
31Lambdaparameter: 43
body: 38
32Literal
33Variable
34ExprTuple37, 39
35Literal
36ExprTuple38, 39
37IndexedVarvariable: 40
index: 43
38IndexedVarvariable: 41
index: 43
39Literal
40Variable
41Variable
42ExprTuple43
43Variable