Nuprl Lemma : iseg_transitivity
∀[T:Type]. ∀l1,l2,l3:T List. (l1 ≤ l2 ⇒ l2 ≤ l3 ⇒ l1 ≤ l3)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
top: Top,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
append_wf,
equal_wf,
list_wf,
exists_wf,
append_assoc,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
Error :universeIsType,
universeEquality,
because_Cache,
natural_numberEquality,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2,l3:T List. (l1 \mleq{} l2 {}\mRightarrow{} l2 \mleq{} l3 {}\mRightarrow{} l1 \mleq{} l3)
Date html generated:
2019_06_20-PM-01_28_06
Last ObjectModification:
2018_09_26-PM-05_37_19
Theory : list_1
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