Nuprl Lemma : band-is-inl-base
∀[a,b:Base].
∀[c:Top]. (a ~ inl outl(a)) ∧ (b ~ inl outl(b)) supposing (a ∧b b) = (inl c) ∈ (Top + Top)
supposing a ∧b b ∈ Top + Top
Proof
Definitions occuring in Statement :
band: p ∧b q,
outl: outl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
member: t ∈ T,
inl: inl x,
union: left + right,
base: Base,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
prop: ℙ,
top: Top,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
outr: outr(x),
so_lambda: λ2x.t[x],
so_apply: x[s],
false: False,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
true: True
Lemmas referenced :
value-type-has-value,
union-value-type,
top_wf,
has-value-band-type,
equal-wf-base-T,
equal-wf-base,
base_wf,
has-value-implies-dec-isinl-2,
equal_wf,
all_wf,
sqequal-wf-base,
not_all_sqequal,
subtype_base_sq,
int_subtype_base,
band-is-inl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
hypothesis,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
sqequalRule,
productElimination,
independent_pairEquality,
sqequalAxiom,
inlEquality,
isect_memberEquality,
voidElimination,
voidEquality,
unionEquality,
baseApply,
closedConclusion,
baseClosed,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
lambdaFormation,
lambdaEquality,
applyLambdaEquality,
natural_numberEquality,
instantiate,
cumulativity,
intEquality,
promote_hyp
Latex:
\mforall{}[a,b:Base].
\mforall{}[c:Top]. (a \msim{} inl outl(a)) \mwedge{} (b \msim{} inl outl(b)) supposing (a \mwedge{}\msubb{} b) = (inl c)
supposing a \mwedge{}\msubb{} b \mmember{} Top + Top
Date html generated:
2017_04_14-AM-07_31_07
Last ObjectModification:
2017_02_27-PM-02_59_36
Theory : bool_1
Home
Index