Nuprl Lemma : sp-meet_wf
∀[f,g:Sierpinski]. (f ∧ g ∈ Sierpinski)
Proof
Definitions occuring in Statement :
sp-meet: f ∧ g,
Sierpinski: Sierpinski,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Sierpinski: Sierpinski,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
sp-meet: f ∧ g,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
rev_uimplies: rev_uimplies(P;Q),
not: ¬A,
false: False,
rev_implies: P ⇐ Q,
btrue: tt,
assert: ↑b,
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
Sierpinski_wf,
quotient-member-eq,
nat_wf,
bool_wf,
iff_wf,
equal-wf-T-base,
two-class-equiv-rel,
Sierpinski-bottom_wf,
coded-pair_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
bfalse_wf,
istype-nat,
equal-Sierpinski-bottom,
istype-assert,
bool_cases_sqequal,
assert_elim,
not_assert_elim,
btrue_neq_bfalse,
code-pair_wf,
iff_weakening_uiff,
assert_wf,
assert_functionality_wrt_uiff,
coded-code-pair
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
promote_hyp,
thin,
productElimination,
isectElimination,
functionEquality,
lambdaEquality_alt,
hypothesisEquality,
baseClosed,
because_Cache,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_functionElimination,
lambdaFormation_alt,
applyEquality,
unionElimination,
instantiate,
cumulativity,
independent_functionElimination,
equalityIstype,
independent_pairFormation,
rename,
voidElimination,
sqequalBase,
productIsType,
functionIsType,
universeIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
natural_numberEquality,
dependent_set_memberEquality_alt,
baseApply,
closedConclusion,
applyLambdaEquality,
setElimination,
independent_pairEquality,
spreadEquality
Latex:
\mforall{}[f,g:Sierpinski]. (f \mwedge{} g \mmember{} Sierpinski)
Date html generated:
2019_10_31-AM-06_35_41
Last ObjectModification:
2018_12_13-PM-03_00_20
Theory : synthetic!topology
Home
Index