Nuprl Lemma : rmin_wf
∀[x,y:ℝ]. (rmin(x;y) ∈ ℝ)
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rmin: rmin(x;y),
real: ℝ,
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
nat_plus: ℕ+,
nat: ℕ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
cand: A c∧ B,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j
Lemmas referenced :
le_weakening,
absval-imin-difference,
le_functionality,
iff_weakening_equal,
mul-imin,
true_wf,
squash_wf,
le_wf,
imax_lb,
nat_wf,
imax_wf,
subtract_wf,
absval_wf,
nat_plus_subtype_nat,
real_wf,
regular-int-seq_wf,
nat_plus_wf,
imin_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
lambdaEquality,
lemma_by_obid,
isectElimination,
applyEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
multiplyEquality,
addEquality,
productElimination,
independent_isectElimination,
independent_pairFormation,
imageElimination,
intEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. (rmin(x;y) \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-06_59_15
Last ObjectModification:
2016_01_17-AM-01_48_11
Theory : reals
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