Nuprl Lemma : neg-bool-trans_wf
neg-bool-trans() ∈ {() ⊢ _:(discr(𝔹) ⟶ discr(𝔹))}
Proof
Definitions occuring in Statement :
neg-bool-trans: neg-bool-trans(),
discrete-cubical-type: discr(T),
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _:A},
trivial-cube-set: (),
bool: 𝔹,
member: t ∈ T
Definitions unfolded in proof :
neg-bool-trans: neg-bool-trans(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
cubical-bool: Bool,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
path-trans_wf,
trivial-cube-set_wf,
cubical-bool_wf,
equiv-path_wf,
bool-negation-equiv_wf,
cubical-term_wf,
cubical-fun_wf,
cubical-type_wf,
discrete-cubical-type_wf,
bool_wf,
discrete-comp_wf,
equal_wf,
squash_wf,
true_wf,
universe-decode-encode,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
cut,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
because_Cache,
natural_numberEquality,
imageMemberEquality,
hypothesisEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
neg-bool-trans() \mmember{} \{() \mvdash{} \_:(discr(\mBbbB{}) {}\mrightarrow{} discr(\mBbbB{}))\}
Date html generated:
2018_05_23-PM-06_27_22
Last ObjectModification:
2018_05_20-PM-09_28_20
Theory : cubical!type!theory
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