Nuprl Lemma : eqtt_assert_2
∀[b:Decision]. uiff(b = tt ∈ Decision;↑b)
Proof
Definitions occuring in Statement :
decision: Decision,
assert: ↑b,
btrue: tt,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
assert: ↑b,
btrue: tt,
decision: Decision,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
true: True,
isl: isl(x),
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
btrue_wf,
and_wf,
equal_wf,
top_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
true_wf,
false_wf,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
unionElimination,
thin,
natural_numberEquality,
extract_by_obid,
hypothesis,
equalitySymmetry,
dependent_set_memberEquality,
equalityTransitivity,
sqequalHypSubstitution,
isectElimination,
unionEquality,
hypothesisEquality,
applyLambdaEquality,
setElimination,
rename,
productElimination,
independent_functionElimination,
voidElimination,
because_Cache,
lambdaFormation,
axiomEquality,
dependent_functionElimination,
baseClosed,
inlEquality,
isect_memberEquality,
voidEquality,
independent_pairEquality
Latex:
\mforall{}[b:Decision]. uiff(b = tt;\muparrow{}b)
Date html generated:
2019_10_15-AM-10_46_59
Last ObjectModification:
2018_08_21-PM-01_57_40
Theory : basic
Home
Index