Nuprl Lemma : subtype_rel-tag-by
∀[T,S:Type]. ∀[z:Atom]. z×T ⊆r z×S supposing T ⊆r S
Proof
Definitions occuring in Statement :
tag-by: z×T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
tag-by: z×T,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
subtype_rel_product,
equal-wf-base,
atom_subtype_base,
set_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
atomEquality,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
cumulativity,
because_Cache,
independent_isectElimination,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T,S:Type]. \mforall{}[z:Atom]. z\mtimes{}T \msubseteq{}r z\mtimes{}S supposing T \msubseteq{}r S
Date html generated:
2018_05_21-PM-08_41_47
Last ObjectModification:
2017_07_26-PM-06_05_39
Theory : general
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