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Expression of type Forall

from the theory of proveit.logic.booleans.conjunction

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 l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [A_1_to_l, B_1_to_m, C_1_to_n]
expr = Forall(instance_param_or_params = [l, m, n], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = And(B_1_to_m), conditions = sub_expr1), domain = Natural)
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_{l, m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\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
2Lambdaparameters: 3
body: 4
3ExprTuple29, 31, 34
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 23
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 24
body: 14
11Operationoperator: 17
operands: 15
12Operationoperator: 17
operands: 16
13Operationoperator: 17
operands: 18
14Conditionalvalue: 19
condition: 20
15ExprTuple29, 21
16ExprTuple31, 21
17Literal
18ExprTuple34, 21
19Operationoperator: 23
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple26
23Literal
24ExprTuple25, 26, 27
25ExprRangelambda_map: 28
start_index: 33
end_index: 29
26ExprRangelambda_map: 30
start_index: 33
end_index: 31
27ExprRangelambda_map: 32
start_index: 33
end_index: 34
28Lambdaparameter: 42
body: 35
29Variable
30Lambdaparameter: 42
body: 36
31Variable
32Lambdaparameter: 42
body: 37
33Literal
34Variable
35IndexedVarvariable: 38
index: 42
36IndexedVarvariable: 39
index: 42
37IndexedVarvariable: 40
index: 42
38Variable
39Variable
40Variable
41ExprTuple42
42Variable