Nuprl Lemma : rstar_functionality
∀[x,y:ℝ]. (x)* = (y)* supposing x = y
Proof
Definitions occuring in Statement :
rstar: (x)*,
req*: x = y,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
req*: x = y,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
all: ∀x:A. B[x],
rstar: (x)*,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
req_witness,
false_wf,
le_wf,
int_upper_wf,
all_wf,
req_wf,
rstar_wf,
int_upper_subtype_nat,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
rename,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
setElimination,
because_Cache,
lambdaEquality,
applyEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. (x)* = (y)* supposing x = y
Date html generated:
2018_05_22-PM-03_18_00
Last ObjectModification:
2017_10_06-PM-06_27_59
Theory : reals_2
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