Nuprl Lemma : member-functions-list
∀n,b:ℕ. ∀f:ℕn ⟶ ℕb. (f ∈ functions-list(n;b))
Proof
Definitions occuring in Statement :
functions-list: functions-list(n;b),
l_member: (x ∈ l),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
false: False,
or: P ∨ Q,
decidable: Dec(P),
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
guard: {T},
not: ¬A
Lemmas referenced :
nat_wf,
equal_wf,
compact-finite,
decidable__equal_int_seg,
decidable__equal_compact_domain,
decidable__l_member,
l_member_wf,
all_wf,
no_repeats_wf,
int_seg_wf,
list_wf,
set_wf,
functions-list_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
voidElimination,
unionElimination,
independent_functionElimination,
dependent_functionElimination,
applyEquality,
functionExtensionality,
productEquality,
lambdaEquality,
sqequalRule,
because_Cache,
rename,
setElimination,
natural_numberEquality,
functionEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productElimination
Latex:
\mforall{}n,b:\mBbbN{}. \mforall{}f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}b. (f \mmember{} functions-list(n;b))
Date html generated:
2018_05_21-PM-08_24_45
Last ObjectModification:
2017_12_14-PM-10_44_03
Theory : general
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