Nuprl Lemma : l-ordered-single
∀[T:Type]. ∀x:T. ∀[R:T ⟶ T ⟶ ℙ]. l-ordered(T;x,y.R[x;y];[x])
Proof
Definitions occuring in Statement :
l-ordered: l-ordered(T;x,y.R[x; y];L),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
l-ordered: l-ordered(T;x,y.R[x; y];L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
squash: ↓T,
true: True,
not: ¬A,
false: False,
uimplies: b supposing a
Lemmas referenced :
l_before_member,
cons_wf,
nil_wf,
l_before_member2,
member_singleton,
l_before_wf,
no_repeats_singleton,
squash_wf,
true_wf,
list_wf,
l_before_antisymmetry
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
cumulativity,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
equalityElimination,
functionEquality,
universeEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
hyp_replacement,
Error :applyLambdaEquality,
voidElimination,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. l-ordered(T;x,y.R[x;y];[x])
Date html generated:
2016_10_25-AM-10_56_35
Last ObjectModification:
2016_07_12-AM-07_03_33
Theory : general
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