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In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.booleans.disjunction import disjunction_from_quantification
In [2]:
# check that the built expression is the same as the stored expression
assert disjunction_from_quantification.expr == stored_expr
assert disjunction_from_quantification.expr._style_id == stored_expr._style_id
print("Passed sanity check: disjunction_from_quantification matches stored_expr")
Passed sanity check: disjunction_from_quantification matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{i, j \in \mathbb{Z}}~\left[\forall_{P~|~i \leq \left(j + 1\right)}~\left(\left[\exists_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right] \Rightarrow \left(P\left(i\right) \lor  P\left(i + 1\right) \lor  \ldots \lor  P\left(j\right)\right)\right)\right]
In [4]:
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 [5]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 6
operand: 2
1ExprTuple2
2Lambdaparameters: 50
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple11, 12
10Lambdaparameter: 44
body: 14
11Operationoperator: 42
operands: 15
12Operationoperator: 42
operands: 16
13ExprTuple44
14Conditionalvalue: 17
condition: 18
15ExprTuple51, 19
16ExprTuple52, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple51, 26
24Operationoperator: 27
operand: 33
25Operationoperator: 29
operands: 30
26Operationoperator: 31
operands: 32
27Literal
28ExprTuple33
29Literal
30ExprTuple34
31Literal
32ExprTuple52, 35
33Lambdaparameter: 46
body: 36
34ExprRangelambda_map: 37
start_index: 51
end_index: 52
35Literal
36Conditionalvalue: 38
condition: 39
37Lambdaparameter: 48
body: 40
38Operationoperator: 44
operand: 46
39Operationoperator: 42
operands: 43
40Operationoperator: 44
operand: 48
41ExprTuple46
42Literal
43ExprTuple46, 47
44Variable
45ExprTuple48
46Variable
47Operationoperator: 49
operands: 50
48Variable
49Literal
50ExprTuple51, 52
51Variable
52Variable