Nuprl Lemma : name-morph-domain-inject
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. Inj(name-morph-domain(f;I);nameset(J);f)
Proof
Definitions occuring in Statement :
name-morph-domain: name-morph-domain(f;I),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
inject: Inj(A;B;f),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
inject: Inj(A;B;f),
all: ∀x:A. B[x],
name-morph-domain: name-morph-domain(f;I),
nameset: nameset(L),
member: t ∈ T,
implies: P ⇒ Q,
name-morph: name-morph(I;J),
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
name-morph-domain_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
member_filter_2,
isname_wf,
l_member_wf,
assert-isname,
nameset_subtype_extd-nameset,
equal_wf,
nameset_wf,
equal_functionality_wrt_subtype_rel2,
extd-nameset_wf,
subtype_base_sq,
nameset_subtype_base,
filter_wf5
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
lambdaEquality,
applyEquality,
sqequalRule,
setEquality,
productElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_set_memberEquality,
instantiate,
cumulativity,
independent_pairFormation
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. Inj(name-morph-domain(f;I);nameset(J);f)
Date html generated:
2016_05_20-AM-09_30_29
Last ObjectModification:
2015_12_28-PM-04_46_53
Theory : cubical!sets
Home
Index