Nuprl Lemma : subtype_rel_record+_easy
∀[T1,T2:𝕌']. ∀[B:T2 ⟶ 𝕌']. ∀[z:Atom]. (T1; z:B[self] ⊆r T2; z:B[self]) supposing T1 ⊆r T2
Proof
Definitions occuring in Statement :
record+: record+,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
subtype_rel_record+,
subtype_rel_self,
subtype_rel_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
sqequalRule,
lambdaEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
instantiate,
axiomEquality,
atomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T1,T2:\mBbbU{}']. \mforall{}[B:T2 {}\mrightarrow{} \mBbbU{}']. \mforall{}[z:Atom]. (T1; z:B[self] \msubseteq{}r T2; z:B[self]) supposing T1 \msubseteq{}r T2
Date html generated:
2016_05_15-PM-06_39_32
Last ObjectModification:
2015_12_27-AM-11_53_03
Theory : general
Home
Index