Nuprl Lemma : select_cons_tl_sq2
∀[i:ℕ]. ∀[x,l:Top]. ([x / l][i + 1] ~ l[i])
Proof
Definitions occuring in Statement :
select: L[n],
cons: [a / b],
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
uimplies: b supposing a,
and: P ∧ Q,
le: A ≤ B,
cand: A c∧ B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
subtract: n - m,
top: Top,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
select-cons-tl,
decidable__lt,
istype-false,
not-lt-2,
condition-implies-le,
minus-add,
istype-void,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
add-subtract-cancel,
istype-top,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
addEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
productElimination,
dependent_functionElimination,
unionElimination,
lambdaFormation_alt,
voidElimination,
independent_functionElimination,
isect_memberEquality_alt,
minusEquality,
axiomSqEquality,
inhabitedIsType,
isectIsTypeImplies
Latex:
\mforall{}[i:\mBbbN{}]. \mforall{}[x,l:Top]. ([x / l][i + 1] \msim{} l[i])
Date html generated:
2020_05_19-PM-09_37_07
Last ObjectModification:
2019_11_13-AM-10_24_52
Theory : list_0
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