Nuprl Lemma : subtype_rel_Form
∀[A,B:Type]. Form(A) ⊆r Form(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
Form: Form(C),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
Form: Form(C),
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
subtype_rel_Formco,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type,
Formco_size_wf,
Form_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
independent_isectElimination,
hypothesis,
sqequalRule,
intEquality,
natural_numberEquality,
cumulativity,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. Form(A) \msubseteq{}r Form(B) supposing A \msubseteq{}r B
Date html generated:
2018_05_21-PM-11_26_37
Last ObjectModification:
2017_10_11-AM-11_28_21
Theory : PZF
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