Nuprl Lemma : cmp-le_wf
∀[T:Type]. ∀[cmp:comparison(T)]. ∀[x,y:cmp-type(T;cmp)]. (cmp-le(cmp;x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
cmp-le: cmp-le(cmp;x;y),
cmp-type: cmp-type(T;cmp),
comparison: comparison(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cmp-type: cmp-type(T;cmp),
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cmp-le: cmp-le(cmp;x;y),
comparison: comparison(T),
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal-wf-T-base,
equal_wf,
equal-wf-base,
cmp-type_wf,
comparison_wf,
le_wf,
squash_wf,
true_wf,
iff_weakening_equal,
minus_functionality_wrt_eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
universeEquality,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
hypothesisEquality,
lambdaFormation,
because_Cache,
rename,
setElimination,
dependent_functionElimination,
independent_functionElimination,
extract_by_obid,
isectElimination,
intEquality,
applyEquality,
baseClosed,
productEquality,
axiomEquality,
cumulativity,
isect_memberEquality,
natural_numberEquality,
functionExtensionality,
minusEquality,
instantiate,
lambdaEquality,
imageElimination,
imageMemberEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[cmp:comparison(T)]. \mforall{}[x,y:cmp-type(T;cmp)]. (cmp-le(cmp;x;y) \mmember{} \mBbbP{})
Date html generated:
2017_04_17-AM-08_27_15
Last ObjectModification:
2017_02_27-PM-04_49_37
Theory : list_1
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