Nuprl Lemma : fseg_cons_left
∀[T:Type]. ∀x:T. ∀[L1,L2:T List]. (fseg(T;[x / L1];L2) ⇒ fseg(T;L1;L2))
Proof
Definitions occuring in Statement :
fseg: fseg(T;L1;L2),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
fseg: fseg(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
append_wf,
cons_wf,
nil_wf,
append_assoc,
equal_wf,
list_wf,
exists_wf,
list_ind_cons_lemma,
list_ind_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}[L1,L2:T List]. (fseg(T;[x / L1];L2) {}\mRightarrow{} fseg(T;L1;L2))
Date html generated:
2016_05_15-PM-03_34_31
Last ObjectModification:
2015_12_27-PM-01_13_34
Theory : general
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