Nuprl Lemma : bpa-equiv_weakening
∀p:{2...}. ∀a,b:basic-padic(p). ((a = b ∈ basic-padic(p)) ⇒ bpa-equiv(p;b;a))
Proof
Definitions occuring in Statement :
bpa-equiv: bpa-equiv(p;x;y),
basic-padic: basic-padic(p),
int_upper: {i...},
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
int_upper: {i...},
guard: {T},
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
uiff: uiff(P;Q),
top: Top,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
bpa-equiv-equiv,
equal_wf,
basic-padic_wf,
int_upper_wf,
and_wf,
bpa-equiv_wf,
subtype_rel_sets,
le_wf,
less_than_wf,
decidable__lt,
false_wf,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
setElimination,
rename,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
sqequalRule,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
applyEquality,
because_Cache,
lambdaEquality,
intEquality,
independent_isectElimination,
setEquality,
unionElimination,
voidElimination,
independent_functionElimination,
isect_memberEquality,
voidEquality
Latex:
\mforall{}p:\{2...\}. \mforall{}a,b:basic-padic(p). ((a = b) {}\mRightarrow{} bpa-equiv(p;b;a))
Date html generated:
2018_05_21-PM-03_25_01
Last ObjectModification:
2018_05_19-AM-08_22_31
Theory : rings_1
Home
Index