Nuprl Lemma : comb_for_rng_when_wf
λr,b,p,z. (when b. p) ∈ r:Rng ⟶ b:𝔹 ⟶ p:|r| ⟶ (↓True) ⟶ |r|
Proof
Definitions occuring in Statement :
rng_when: rng_when,
rng: Rng,
rng_car: |r|,
bool: 𝔹,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rng: Rng
Lemmas referenced :
rng_when_wf,
squash_wf,
true_wf,
rng_car_wf,
bool_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
setElimination,
rename
Latex:
\mlambda{}r,b,p,z. (when b. p) \mmember{} r:Rng {}\mrightarrow{} b:\mBbbB{} {}\mrightarrow{} p:|r| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |r|
Date html generated:
2016_05_15-PM-00_28_54
Last ObjectModification:
2015_12_26-PM-11_58_20
Theory : rings_1
Home
Index