Nuprl Lemma : l-ordered-from-upto-lt-true
∀[n,m:ℤ]. (l-ordered(ℤ;x,y.x < y;[n, m)) ⇐⇒ True)
Proof
Definitions occuring in Statement :
l-ordered: l-ordered(T;x,y.R[x; y];L),
from-upto: [n, m),
less_than: a < b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
true: True,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rev_implies: P ⇐ Q,
l-ordered: l-ordered(T;x,y.R[x; y];L),
all: ∀x:A. B[x]
Lemmas referenced :
l-ordered_wf,
from-upto_wf,
subtype_rel_list,
and_wf,
le_wf,
less_than_wf,
l-ordered-from-upto-lt,
true_wf,
member-less_than,
l_before_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
applyEquality,
setEquality,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
because_Cache,
sqequalRule,
productElimination,
independent_pairEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. (l-ordered(\mBbbZ{};x,y.x < y;[n, m)) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_15-PM-04_37_12
Last ObjectModification:
2015_12_27-PM-02_44_17
Theory : general
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