Nuprl Lemma : iseg_weakening2
∀[T:Type]. ∀l1,l2:T List. l1 ≤ l2 supposing l1 = l2 ∈ (T List)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
iseg_weakening,
iff_weakening_equal,
list_wf,
true_wf,
squash_wf,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
applyEquality,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. l1 \mleq{} l2 supposing l1 = l2
Date html generated:
2016_05_14-PM-01_31_53
Last ObjectModification:
2016_01_15-AM-08_26_57
Theory : list_1
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