Nuprl Lemma : min_w_ord_wf
∀[T:Type]. ∀[t1,t2:T]. ∀[f:T ⟶ ℤ]. (min_w_ord(t1;t2;f) ∈ T)
Proof
Definitions occuring in Statement :
min_w_ord: min_w_ord(t1;t2;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
min_w_ord: min_w_ord(t1;t2;f),
so_apply: x[s],
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,
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T}
Lemmas referenced :
lt_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
btrue_wf,
assert_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int,
bfalse_wf,
le_int_wf,
le_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
functionEquality,
intEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t1,t2:T]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. (min\_w\_ord(t1;t2;f) \mmember{} T)
Date html generated:
2016_05_16-AM-08_44_00
Last ObjectModification:
2015_12_28-PM-06_41_37
Theory : labeled!trees
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