Nuprl Lemma : assert-eq-cname
∀[x,y:Cname]. uiff(↑eq-cname(x;y);x = y ∈ Cname)
Proof
Definitions occuring in Statement :
eq-cname: eq-cname(x;y),
coordinate_name: Cname,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eq-cname: eq-cname(x;y),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
deq: EqDecider(T),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
coordinate_name_wf,
iff_weakening_uiff,
assert_wf,
cname_deq_wf,
deq_wf,
assert-deq,
assert_witness,
uiff_wf,
eq-cname_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
addLevel,
productElimination,
independent_isectElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
independent_functionElimination,
cumulativity,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:Cname]. uiff(\muparrow{}eq-cname(x;y);x = y)
Date html generated:
2017_10_05-AM-10_04_49
Last ObjectModification:
2017_07_28-AM-11_15_50
Theory : cubical!sets
Home
Index