Nuprl Lemma : fseg_weakening
∀[T:Type]. ∀l1,l2:T List. fseg(T;l1;l2) supposing l1 = l2 ∈ (T List)
Proof
Definitions occuring in Statement :
fseg: fseg(T;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 :
fseg: fseg(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
exists: ∃x:A. B[x],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
prop: ℙ
Lemmas referenced :
nil_wf,
list_ind_nil_lemma,
equal_wf,
list_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
dependent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. fseg(T;l1;l2) supposing l1 = l2
Date html generated:
2016_05_15-PM-03_34_46
Last ObjectModification:
2015_12_27-PM-01_13_42
Theory : general
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