Nuprl Lemma : init-seg-nat-seq-append-implies-left
∀a,b,s:finite-nat-seq(). ((↑init-seg-nat-seq(a**b;s)) ⇒ (↑init-seg-nat-seq(a;s)))
Proof
Definitions occuring in Statement :
init-seg-nat-seq: init-seg-nat-seq(f;g),
append-finite-nat-seq: f**g,
finite-nat-seq: finite-nat-seq(),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
assert-init-seg-nat-seq,
append-finite-nat-seq_wf,
equal_wf,
squash_wf,
true_wf,
finite-nat-seq_wf,
append-finite-nat-seq-assoc,
iff_weakening_equal,
exists_wf,
assert_wf,
init-seg-nat-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
isectElimination,
because_Cache,
dependent_pairFormation,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}a,b,s:finite-nat-seq(). ((\muparrow{}init-seg-nat-seq(a**b;s)) {}\mRightarrow{} (\muparrow{}init-seg-nat-seq(a;s)))
Date html generated:
2017_04_20-AM-07_30_09
Last ObjectModification:
2017_02_27-PM-06_00_43
Theory : continuity
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