Nuprl Lemma : comb_for_bimplies_wf
λp,q,z. (p ⇒b q) ∈ p:𝔹 ⟶ q:𝔹 supposing ↑p ⟶ (↓True) ⟶ 𝔹
Proof
Definitions occuring in Statement :
bimplies: p ⇒b q,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
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,
uimplies: b supposing a
Lemmas referenced :
bimplies_wf,
squash_wf,
true_wf,
assert_wf,
bool_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,
sqequalRule,
Error :isectIsType,
Error :inhabitedIsType
Latex:
\mlambda{}p,q,z. (p {}\mRightarrow{}\msubb{} q) \mmember{} p:\mBbbB{} {}\mrightarrow{} q:\mBbbB{} supposing \muparrow{}p {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbB{}
Date html generated:
2019_06_20-AM-11_31_15
Last ObjectModification:
2018_10_09-AM-09_29_13
Theory : bool_1
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