Nuprl Lemma : comb_for_fun_exp_wf
λT,n,f,z. f^n ∈ T:Type ⟶ n:ℕ ⟶ f:(T ⟶ T) ⟶ (↓True) ⟶ T ⟶ T
Proof
Definitions occuring in Statement :
fun_exp: f^n,
nat: ℕ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
fun_exp_wf,
squash_wf,
true_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
Error :functionIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mlambda{}T,n,f,z. f\^{}n \mmember{} T:Type {}\mrightarrow{} n:\mBbbN{} {}\mrightarrow{} f:(T {}\mrightarrow{} T) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} T {}\mrightarrow{} T
Date html generated:
2019_06_20-PM-00_26_41
Last ObjectModification:
2018_09_28-PM-11_40_51
Theory : fun_1
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