Nuprl Lemma : cons-proper-iseg
∀[T:Type]. ∀L1,L2:T List. ∀a,b:T. ([a / L1] < [b / L2] ⇐⇒ L1 < L2 ∧ (a = b ∈ T))
Proof
Definitions occuring in Statement :
proper-iseg: L1 < L2,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
proper-iseg: L1 < L2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
iff_wf,
cons_iseg,
tl_wf,
reduce_tl_cons_lemma,
not_wf,
iseg_wf,
and_wf,
list_wf,
equal_wf,
true_wf,
squash_wf,
cons_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
independent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
voidElimination,
dependent_functionElimination,
isect_memberEquality,
voidEquality,
dependent_set_memberEquality,
setElimination,
rename,
setEquality,
addLevel,
impliesFunctionality,
andLevelFunctionality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. \mforall{}a,b:T. ([a / L1] < [b / L2] \mLeftarrow{}{}\mRightarrow{} L1 < L2 \mwedge{} (a = b))
Date html generated:
2016_05_14-PM-03_04_07
Last ObjectModification:
2016_01_15-AM-07_23_17
Theory : list_1
Home
Index