Nuprl Lemma : msep-symm
∀[X:Type]. ∀d:metric(X). ∀x,y:X. uiff(x # y;y # x)
Proof
Definitions occuring in Statement :
msep: x # y,
metric: metric(X),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
msep: x # y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
sq_stable__rless,
int-to-real_wf,
mdist_wf,
rless_wf,
metric_wf,
istype-universe,
rless_functionality,
req_weakening,
mdist-symm
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation_alt,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
universeIsType,
inhabitedIsType,
instantiate,
universeEquality,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}[X:Type]. \mforall{}d:metric(X). \mforall{}x,y:X. uiff(x \# y;y \# x)
Date html generated:
2019_10_29-AM-11_01_23
Last ObjectModification:
2019_10_02-AM-09_42_35
Theory : reals
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