Nuprl Lemma : rmin-stable-cases
∀a,b:ℝ. ∀P:Type. (Stable{P} ⇒ (((rmin(a;b) = a) ⇒ P) ∧ ((rmin(a;b) = b) ⇒ P)) ⇒ P)
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
req: x = y,
real: ℝ,
stable: Stable{P},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
or: P ∨ Q,
not: ¬A,
false: False,
stable: Stable{P},
uimplies: b supposing a
Lemmas referenced :
req_wf,
rmin_wf,
stable_wf,
istype-universe,
real_wf,
false_wf,
not_wf,
istype-void,
rmin-classical-cases,
minimal-double-negation-hyp-elim,
minimal-not-not-excluded-middle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
productIsType,
functionIsType,
universeIsType,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
instantiate,
universeEquality,
inhabitedIsType,
unionEquality,
functionEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
unionElimination,
voidElimination,
unionIsType
Latex:
\mforall{}a,b:\mBbbR{}. \mforall{}P:Type. (Stable\{P\} {}\mRightarrow{} (((rmin(a;b) = a) {}\mRightarrow{} P) \mwedge{} ((rmin(a;b) = b) {}\mRightarrow{} P)) {}\mRightarrow{} P)
Date html generated:
2019_10_29-AM-09_38_49
Last ObjectModification:
2019_07_29-PM-03_16_31
Theory : reals
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