Nuprl Lemma : fseg_cons2
∀[T:Type]. ∀x:T. ∀[L1,L2:T List]. (fseg(T;L1;L2) ⇒ fseg(T;L1;[x / 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,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
cons_wf,
list_ind_cons_lemma,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
list_wf,
append_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
lambdaEquality,
imageElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}[L1,L2:T List]. (fseg(T;L1;L2) {}\mRightarrow{} fseg(T;L1;[x / L2]))
Date html generated:
2018_05_21-PM-06_30_11
Last ObjectModification:
2017_07_26-PM-04_50_34
Theory : general
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