Nuprl Lemma : name-morph_subtype
∀[I,J,A,B:Cname List].
(name-morph(I;J) ⊆r name-morph(A;B)) supposing ((nameset(A) ⊆r nameset(I)) and (nameset(J) ⊆r nameset(B)))
Proof
Definitions occuring in Statement :
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
extd-nameset: extd-nameset(L),
and: P ∧ Q,
name-morph: name-morph(I;J),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
subtype_rel_wf,
nameset_wf,
subtype_rel_b-union,
int_seg_wf,
subtype_rel_self,
name-morph_wf,
subtype_rel_dep_function,
extd-nameset_wf,
assert_wf,
isname_wf,
subtype_base_sq,
extd-nameset_subtype_base,
nameset_subtype_base,
equal_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
applyEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
instantiate,
cumulativity,
functionEquality
Latex:
\mforall{}[I,J,A,B:Cname List].
(name-morph(I;J) \msubseteq{}r name-morph(A;B)) supposing
((nameset(A) \msubseteq{}r nameset(I)) and
(nameset(J) \msubseteq{}r nameset(B)))
Date html generated:
2016_05_20-AM-09_29_45
Last ObjectModification:
2015_12_28-PM-04_47_09
Theory : cubical!sets
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