Nuprl Lemma : t-sqle-base
∀[T:Type]. ∀a,b:T. (t-sqle(T;a;b) ⇒ (a ≤ b)) supposing T ⊆r Base
Proof
Definitions occuring in Statement :
t-sqle: t-sqle(T;a;b),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
base: Base,
universe: Type,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
t-sqle: t-sqle(T;a;b),
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
per-class-base,
t-sqle_wf,
subtype_rel_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
lemma_by_obid,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
sqequalRule,
axiomSqleEquality,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}a,b:T. (t-sqle(T;a;b) {}\mRightarrow{} (a \mleq{} b)) supposing T \msubseteq{}r Base
Date html generated:
2016_05_13-PM-04_12_56
Last ObjectModification:
2015_12_26-AM-11_11_34
Theory : subtype_1
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