Nuprl Lemma : name-morph-ext
∀[I,J:Cname List]. ∀[f,g:name-morph(I;J)].
f = g ∈ name-morph(I;J) supposing ∀x:nameset(I). ((f x) = (g x) ∈ extd-nameset(J))
Proof
Definitions occuring in Statement :
name-morph: name-morph(I;J),
extd-nameset: extd-nameset(L),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
name-morph: name-morph(I;J),
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morphs-equal,
equal_wf,
squash_wf,
true_wf,
extd-nameset_wf,
iff_weakening_equal,
nameset_wf,
all_wf,
name-morph_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
hypothesis,
independent_isectElimination,
functionExtensionality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f,g:name-morph(I;J)]. f = g supposing \mforall{}x:nameset(I). ((f x) = (g x))
Date html generated:
2017_10_05-AM-10_05_32
Last ObjectModification:
2017_07_28-AM-11_16_05
Theory : cubical!sets
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