Nuprl Lemma : unit-ss-eq
∀[t,t':{t:ℝ| t ∈ [r0, r1]} ]. uiff(t = t';t ≡ t')
Proof
Definitions occuring in Statement :
unit-ss: 𝕀,
ss-eq: x ≡ y,
rccint: [l, u],
i-member: r ∈ I,
req: x = y,
int-to-real: r(n),
real: ℝ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
unit-ss: 𝕀,
ss-eq: x ≡ y,
all: ∀x:A. B[x],
member: t ∈ T,
real-ss: ℝ,
set-ss: {x:ss | P[x]},
ss-sep: x # y,
mk-ss: Point=P #=Sep cotrans=C,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
iff: P ⇐⇒ Q,
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
member_rccint_lemma,
rec_select_update_lemma,
rneq_irrefl,
rneq_functionality,
req_weakening,
req_inversion,
rneq_wf,
req_wf,
req_witness,
istype-void,
real_wf,
rleq_wf,
int-to-real_wf,
req-iff-not-rneq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
isect_memberFormation_alt,
independent_pairFormation,
lambdaFormation_alt,
setElimination,
rename,
productElimination,
isectElimination,
hypothesisEquality,
independent_functionElimination,
because_Cache,
independent_isectElimination,
universeIsType,
voidElimination,
lambdaEquality_alt,
functionIsTypeImplies,
inhabitedIsType,
functionIsType,
independent_pairEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
setIsType,
productIsType,
natural_numberEquality
Latex:
\mforall{}[t,t':\{t:\mBbbR{}| t \mmember{} [r0, r1]\} ]. uiff(t = t';t \mequiv{} t')
Date html generated:
2020_05_20-PM-01_20_07
Last ObjectModification:
2020_01_06-PM-05_14_29
Theory : intuitionistic!topology
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