Nuprl Lemma : prank-pvar
∀[a:formula()]. uiff(prank(a) = 0 ∈ ℤ;↑pvar?(a))
Proof
Definitions occuring in Statement :
prank: prank(x),
pvar?: pvar?(v),
formula: formula(),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
implies: P ⇒ Q,
prank: prank(x),
pvar: pvar(name),
formula_ind: formula_ind,
pvar?: pvar?(v),
pi1: fst(t),
eq_atom: x =a y,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
true: True,
prop: ℙ,
pnot: pnot(sub),
bfalse: ff,
false: False,
nat: ℕ,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
pand: pand(left;right),
por: por(left;right),
pimp: pimp(left;right),
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
squash: ↓T,
iff: P ⇐⇒ Q,
sq_type: SQType(T),
rev_implies: P ⇐ Q
Lemmas referenced :
formula-induction,
uiff_wf,
equal-wf-T-base,
prank_wf,
assert_wf,
pvar?_wf,
formula_wf,
equal-wf-base,
true_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
false_wf,
imax_wf,
assert_witness,
nat_wf,
ifthenelse_wf,
le_int_wf,
bnot_wf,
not_wf,
le_wf,
le_weakening2,
decidable__lt,
equal_wf,
squash_wf,
add_functionality_wrt_eq,
imax_unfold,
iff_weakening_equal,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
intEquality,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
baseClosed,
independent_functionElimination,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
atomEquality,
productElimination,
applyLambdaEquality,
setElimination,
rename,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
addEquality,
independent_pairEquality,
unionElimination,
imageElimination,
universeEquality,
imageMemberEquality,
instantiate,
cumulativity,
impliesFunctionality
Latex:
\mforall{}[a:formula()]. uiff(prank(a) = 0;\muparrow{}pvar?(a))
Date html generated:
2018_05_21-PM-08_53_20
Last ObjectModification:
2017_07_26-PM-06_17_05
Theory : general
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