Nuprl Lemma : step-function-example-member
1 ∈ corec(X.step-function-example(X))
Proof
Definitions occuring in Statement :
step-function-example: step-function-example(X),
corec: corec(T.F[T]),
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
so_apply: x[s],
uimplies: b supposing a,
step-function-example: step-function-example(X),
step-function: step-function(T;transition;X),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
exists: ∃x:A. B[x],
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
corec: corec(T.F[T]),
all: ∀x:A. B[x],
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
sq_type: SQType(T),
subtract: n - m
Lemmas referenced :
top_wf,
primrec_wf,
primrec-unroll-1,
isect2_wf,
exists_wf,
subtype_rel_wf,
corec_wf,
isect2_subtype_rel3,
equal-wf-T-base,
equal-wf-base,
equal_wf,
and_wf,
or_wf,
bool_wf,
nat_wf,
int_term_value_add_lemma,
itermAdd_wf,
decidable__lt,
primrec0_lemma,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
le_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
int_seg_subtype,
decidable__equal_int,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
int_seg_properties,
int_seg_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
lelt_wf,
false_wf,
step-function-example-monotone,
step-function-example_wf,
subtype_corec
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesisEquality,
hypothesis,
universeEquality,
independent_isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
introduction,
imageMemberEquality,
baseClosed,
dependent_pairFormation,
isect_memberEquality,
unionElimination,
equalityElimination,
because_Cache,
setElimination,
rename,
intWeakElimination,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
applyEquality,
setEquality,
hypothesis_subsumption,
instantiate,
addEquality,
inlFormation,
productEquality,
cumulativity,
promote_hyp,
inrFormation
Latex:
1 \mmember{} corec(X.step-function-example(X))
Date html generated:
2016_05_15-PM-10_11_50
Last ObjectModification:
2016_01_16-PM-04_11_52
Theory : eval!all
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