Nuprl Lemma : name-morphs-equal
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ∀[g:nameset(I) ⟶ extd-nameset(J)].
f = g ∈ name-morph(I;J) supposing f = g ∈ (nameset(I) ⟶ 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],
function: x:A ⟶ B[x],
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),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
nameset_wf,
assert_wf,
isname_wf,
equal_wf,
extd-nameset_wf,
name-morph_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
functionEquality,
applyEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[g:nameset(I) {}\mrightarrow{} extd-nameset(J)]. f = g supposing f = g
Date html generated:
2016_05_20-AM-09_29_38
Last ObjectModification:
2015_12_28-PM-04_47_35
Theory : cubical!sets
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