Nuprl Lemma : comb_for_ifthenelse_wf
λb,A,p,q,z. if b then p else q fi ∈ b:𝔹 ⟶ A:Type ⟶ p:A ⟶ q:A ⟶ (↓True) ⟶ A
Proof
Definitions occuring in Statement :
ifthenelse: if b then t else f fi ,
bool: 𝔹,
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 :
ifthenelse_wf,
squash_wf,
true_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality
Latex:
\mlambda{}b,A,p,q,z. if b then p else q fi \mmember{} b:\mBbbB{} {}\mrightarrow{} A:Type {}\mrightarrow{} p:A {}\mrightarrow{} q:A {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} A
Date html generated:
2018_05_21-PM-06_20_14
Last ObjectModification:
2018_05_19-PM-05_32_21
Theory : list!
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