Nuprl Lemma : t-sqle_reflexive
∀[T:Type]. ∀a:T. t-sqle(T;a;a)
Proof
Definitions occuring in Statement :
t-sqle: t-sqle(T;a;b),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
t-sqle: t-sqle(T;a;b),
squash: ↓T,
exists: ∃x:A. B[x],
per-class: per-class(T;a),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
implies: P ⇒ Q
Lemmas referenced :
sq_stable__t-sqle,
base_wf,
subtype_rel_b-union-right,
per-class_wf,
exists_wf,
sqle_wf_base,
is-exception_wf,
has-value_wf_base,
squash-per-class
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
imageElimination,
hypothesis,
imageMemberEquality,
baseClosed,
universeEquality,
rename,
dependent_pairFormation,
divergentSqle,
sqleReflexivity,
setElimination,
cumulativity,
applyEquality,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}a:T. t-sqle(T;a;a)
Date html generated:
2016_05_13-PM-04_12_50
Last ObjectModification:
2016_01_14-PM-07_29_11
Theory : subtype_1
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