Nuprl Lemma : cmp-type_wf
∀[T:Type]. ∀cmp:comparison(T). (cmp-type(T;cmp) ∈ Type)
Proof
Definitions occuring in Statement :
cmp-type: cmp-type(T;cmp),
comparison: comparison(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
cmp-type: cmp-type(T;cmp),
so_lambda: λ2x y.t[x; y],
comparison: comparison(T),
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
comparison_wf,
comparison-equiv,
equal-wf-T-base,
quotient_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
intEquality,
applyEquality,
setElimination,
rename,
baseClosed,
hypothesis,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}cmp:comparison(T). (cmp-type(T;cmp) \mmember{} Type)
Date html generated:
2016_05_14-PM-02_37_32
Last ObjectModification:
2016_01_15-AM-07_41_54
Theory : list_1
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