Nuprl Lemma : Leibniz-type_wf
∀[T:𝕌']. (Leibniz-type{i:l}(T) ∈ 𝕌')
Proof
Definitions occuring in Statement :
Leibniz-type: Leibniz-type{i:l}(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Leibniz-type: Leibniz-type{i:l}(T),
exists: ∃x:A. B[x],
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
subtype_rel_self,
iff_wf,
equal_wf,
not_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
functionEquality,
hypothesisEquality,
universeEquality,
cumulativity,
applyEquality,
hypothesis,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
unionEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:\mBbbU{}']. (Leibniz-type\{i:l\}(T) \mmember{} \mBbbU{}')
Date html generated:
2019_10_31-AM-07_25_47
Last ObjectModification:
2019_09_19-PM-04_36_23
Theory : constructive!algebra
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