Nuprl Lemma : id-morph_wf
∀[I:Cname List]. (1 ∈ name-morph(I;I))
Proof
Definitions occuring in Statement :
id-morph: 1,
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
id-morph: 1,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
nameset_subtype_extd-nameset,
nameset_wf,
equal_wf,
extd-nameset_wf,
assert_wf,
all_wf,
isname_wf,
list_wf,
coordinate_name_wf,
subtype_base_sq,
extd-nameset_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
lambdaEquality,
hypothesisEquality,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaFormation,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[I:Cname List]. (1 \mmember{} name-morph(I;I))
Date html generated:
2016_05_20-AM-09_30_57
Last ObjectModification:
2015_12_28-PM-04_47_04
Theory : cubical!sets
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