Nuprl Lemma : bool-negation-equiv_wf
bool-negation-equiv(()) ∈ {() ⊢ _:Equiv(decode(Bool);decode(Bool))}
Proof
Definitions occuring in Statement :
bool-negation-equiv: bool-negation-equiv(X),
cubical-bool: Bool,
universe-decode: decode(t),
cubical-equiv: Equiv(T;A),
cubical-term: {X ⊢ _:A},
trivial-cube-set: (),
member: t ∈ T
Definitions unfolded in proof :
bool-negation-equiv: bool-negation-equiv(X),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cubical-bool: Bool
Lemmas referenced :
bijection-equiv_wf,
bool_wf,
bnot_wf,
equal_wf,
squash_wf,
true_wf,
bnot_bnot_elim,
iff_weakening_equal,
trivial-cube-set_wf,
cubical-term_wf,
cubical-type_wf,
cubical_set_wf,
cubical-equiv_wf,
discrete-cubical-type_wf,
discrete-comp_wf,
universe-decode-encode
Rules used in proof :
cut,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
lambdaEquality,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
hyp_replacement,
instantiate
Latex:
bool-negation-equiv(()) \mmember{} \{() \mvdash{} \_:Equiv(decode(Bool);decode(Bool))\}
Date html generated:
2017_10_05-AM-10_01_32
Last ObjectModification:
2017_03_03-AM-01_39_37
Theory : cubical!type!theory
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