Nuprl Lemma : band-sqequal-inl
∀[a,b,c:Base]. {(a ~ inl outl(a)) ∧ (b ~ inl outl(b))} supposing a ∧b b ~ inl c
Proof
Definitions occuring in Statement :
band: p ∧b q,
outl: outl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
inl: inl x,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
guard: {T},
cand: A c∧ B,
or: P ∨ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
outr: outr(x),
false: False,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
true: True,
sq_type: SQType(T),
bfalse: ff,
outl: outl(x)
Lemmas referenced :
has-value-band-type,
union-value-type,
base_wf,
value-type-has-value,
top_wf,
has-value-implies-dec-isinl-2,
equal_wf,
sqequal-wf-base,
all_wf,
not_all_sqequal,
int_subtype_base,
subtype_base_sq
Rules used in proof :
because_Cache,
isect_memberEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalIntensionalEquality,
axiomSqEquality,
independent_pairEquality,
productElimination,
equalitySymmetry,
equalityTransitivity,
hypothesisEquality,
inlEquality,
independent_isectElimination,
voidEquality,
unionEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution,
independent_pairFormation,
unionElimination,
independent_functionElimination,
dependent_functionElimination,
lambdaFormation,
lambdaEquality,
voidElimination,
promote_hyp,
intEquality,
cumulativity,
instantiate,
natural_numberEquality
Latex:
\mforall{}[a,b,c:Base]. \{(a \msim{} inl outl(a)) \mwedge{} (b \msim{} inl outl(b))\} supposing a \mwedge{}\msubb{} b \msim{} inl c
Date html generated:
2019_06_20-AM-11_32_18
Last ObjectModification:
2018_10_11-PM-06_54_13
Theory : bool_1
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