Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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 A, C, ExprRange, IndexedVar, Variable, m
from proveit.logic import Forall, Implies
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [C], instance_expr = C, condition = ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), C), one, m))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{C~|~\left(A_{1} \Rightarrow C\right), \left(A_{2} \Rightarrow C\right), \ldots, \left(A_{m} \Rightarrow C\right)}~C

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 17 body: 5
4	ExprTuple	17
5	Conditional	value: 17 condition: 6
6	Operation	operator: 7 operands: 8
7	Literal
8	ExprTuple	9
9	ExprRange	lambda_map: 10 start_index: 11 end_index: 12
10	Lambda	parameter: 20 body: 13
11	Literal
12	Variable
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	IndexedVar	variable: 18 index: 20
17	Variable
18	Variable
19	ExprTuple	20
20	Variable