Nuprl Lemma : init-seg-nat-seq_wf
∀[f,g:finite-nat-seq()]. (init-seg-nat-seq(f;g) ∈ 𝔹)
Proof
Definitions occuring in Statement :
init-seg-nat-seq: init-seg-nat-seq(f;g),
finite-nat-seq: finite-nat-seq(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
init-seg-nat-seq: init-seg-nat-seq(f;g),
finite-nat-seq: finite-nat-seq(),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
prop: ℙ,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
ble_wf,
bool_wf,
eqtt_to_assert,
equal-upto-finite-nat-seq_wf,
int_seg_wf,
equal_wf,
finite-nat-seq_wf,
assert-ble,
subtype_rel_dep_function,
nat_wf,
int_seg_subtype,
false_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
independent_isectElimination,
functionExtensionality,
applyEquality,
natural_numberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
lambdaEquality,
independent_pairFormation
Latex:
\mforall{}[f,g:finite-nat-seq()]. (init-seg-nat-seq(f;g) \mmember{} \mBbbB{})
Date html generated:
2017_04_20-AM-07_29_29
Last ObjectModification:
2017_02_27-PM-06_00_29
Theory : continuity
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