Nuprl Lemma : comb_for_band_wf
λp,q,z. (p ∧b q) ∈ p:𝔹 ⟶ q:𝔹 ⟶ (↓True) ⟶ 𝔹
Proof
Definitions occuring in Statement :
band: p ∧b q,
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
Lemmas referenced :
band_wf,
squash_wf,
true_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry
Latex:
\mlambda{}p,q,z. (p \mwedge{}\msubb{} q) \mmember{} p:\mBbbB{} {}\mrightarrow{} q:\mBbbB{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbB{}
Date html generated:
2016_05_13-PM-03_56_02
Last ObjectModification:
2015_12_26-AM-10_52_46
Theory : bool_1
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