Nuprl Lemma : band-to-and
∀[a,b:𝔹]. {(a ~ tt) ∧ (b ~ tt)} supposing a ∧b b ~ tt
Proof
Definitions occuring in Statement :
band: p ∧b q,
btrue: tt,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
subtype_rel: A ⊆r B,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
thin,
because_Cache,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
extract_by_obid,
isectElimination,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
independent_pairFormation,
independent_pairEquality,
sqequalAxiom,
sqequalIntensionalEquality,
applyEquality,
baseClosed,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
isect_memberEquality,
baseApply,
closedConclusion
Latex:
\mforall{}[a,b:\mBbbB{}]. \{(a \msim{} tt) \mwedge{} (b \msim{} tt)\} supposing a \mwedge{}\msubb{} b \msim{} tt
Date html generated:
2017_10_01-AM-09_12_23
Last ObjectModification:
2017_07_26-PM-04_48_04
Theory : general
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