Nuprl Lemma : polymorphic-constant-nat
∀f:⋂A:Type. (A ⟶ ℕ). ∃n:ℕ. ∀A:Type. ∀x:A. ((f x) = n ∈ ℕ)
Proof
Definitions occuring in Statement :
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
polymorphic-constant,
nat_wf,
nat-mono,
set-value-type,
le_wf,
int-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
independent_pairFormation,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
dependent_functionElimination,
isectEquality,
universeEquality,
cumulativity,
functionEquality
Latex:
\mforall{}f:\mcap{}A:Type. (A {}\mrightarrow{} \mBbbN{}). \mexists{}n:\mBbbN{}. \mforall{}A:Type. \mforall{}x:A. ((f x) = n)
Date html generated:
2018_05_21-PM-01_11_49
Last ObjectModification:
2018_05_01-PM-04_36_57
Theory : num_thy_1
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