Nuprl Lemma : subtype_imp-type
∀[A,B:Type]. (B ⊆r imp-type(A;B))
Proof
Definitions occuring in Statement :
imp-type: imp-type(A;B),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
imp-type: imp-type(A;B),
so_lambda: λ2x y.t[x; y],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
rel_implies: R1 => R2,
infix_ap: x f y
Lemmas referenced :
imp-type_wf,
quotient-member-eq,
base_wf,
least-equiv_wf,
equal-wf-base,
least-equiv-is-equiv,
implies-least-equiv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaEquality_alt,
Error :universeIsType,
hypothesisEquality,
sqequalRule,
axiomEquality,
hypothesis,
Error :inhabitedIsType,
sqequalHypSubstitution,
Error :isect_memberEquality_alt,
isectElimination,
thin,
Error :isectIsTypeImplies,
universeEquality,
pointwiseFunctionalityForEquality,
extract_by_obid,
applyEquality,
closedConclusion,
functionEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
Error :lambdaFormation_alt,
Error :equalityIsType4
Latex:
\mforall{}[A,B:Type]. (B \msubseteq{}r imp-type(A;B))
Date html generated:
2019_06_20-PM-02_01_42
Last ObjectModification:
2018_10_14-PM-05_40_29
Theory : relations2
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