Nuprl Lemma : rleq*_weakening_equal
∀[x,y:ℝ*]. ((x = y ∈ ℝ*) ⇒ x ≤ y)
Proof
Definitions occuring in Statement :
rleq*: x ≤ y,
real*: ℝ*,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
rleq*: x ≤ y,
rrel*: R*(x,y),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x],
real*: ℝ*,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rleq*_wf,
squash_wf,
true_wf,
iff_weakening_equal,
false_wf,
le_wf,
rleq_weakening_equal,
subtype_rel_self,
nat_wf,
int_upper_wf,
all_wf,
rleq_wf,
int_upper_subtype_nat,
equal_wf,
real*_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
independent_pairFormation,
setElimination,
rename
Latex:
\mforall{}[x,y:\mBbbR{}*]. ((x = y) {}\mRightarrow{} x \mleq{} y)
Date html generated:
2018_05_22-PM-03_19_54
Last ObjectModification:
2017_10_06-PM-05_13_34
Theory : reals_2
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