Nuprl Lemma : comb_for_choose_wf
λn,i,z. choose(n;i) ∈ n:ℕ ⟶ i:{0...n} ⟶ (↓True) ⟶ ℕ
Proof
Definitions occuring in Statement :
choose: choose(n;i),
int_iseg: {i...j},
nat: ℕ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
nat: ℕ
Lemmas referenced :
choose_wf,
squash_wf,
true_wf,
int_iseg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
natural_numberEquality,
setElimination,
rename
Latex:
\mlambda{}n,i,z. choose(n;i) \mmember{} n:\mBbbN{} {}\mrightarrow{} i:\{0...n\} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbN{}
Date html generated:
2016_05_15-PM-00_26_34
Last ObjectModification:
2015_12_26-PM-11_59_39
Theory : rings_1
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