Nuprl Lemma : meq_weakening
∀[X:Type]. ∀[d:metric(X)]. ∀[x,y:X]. x ≡ y supposing x = y ∈ X
Proof
Definitions occuring in Statement :
meq: x ≡ y,
metric: metric(X),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
meq: x ≡ y,
metric: metric(X)
Lemmas referenced :
meq_wf,
squash_wf,
true_wf,
metric_wf,
istype-universe,
subtype_rel_self,
iff_weakening_equal,
meq-same,
req_witness,
int-to-real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
applyEquality,
thin,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
inhabitedIsType,
instantiate,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
because_Cache,
independent_isectElimination,
productElimination,
independent_functionElimination,
setElimination,
rename,
equalityIstype,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x,y:X]. x \mequiv{} y supposing x = y
Date html generated:
2019_10_29-AM-10_55_56
Last ObjectModification:
2019_10_02-AM-09_37_11
Theory : reals
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