Expression of type Lambda

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, Conditional, ExprRange, IndexedVar, Lambda, Variable, m
from proveit.logic import And, Implies
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(C, Conditional(C, And(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())

C \mapsto \left\{C \textrm{ if } \left(A_{1} \Rightarrow C\right) \land  \left(A_{2} \Rightarrow C\right) \land  \ldots \land  \left(A_{m} \Rightarrow C\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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