Nuprl Lemma : step-function-example-monotone
Monotone(T.step-function-example(T))
Proof
Definitions occuring in Statement :
step-function-example: step-function-example(X),
type-monotone: Monotone(T.F[T])
Definitions unfolded in proof :
type-monotone: Monotone(T.F[T]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
step-function-example: step-function-example(X),
step-function: step-function(T;transition;X),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
int_seg: {i..j-},
so_apply: x[s],
or: P ∨ Q,
exists: ∃x:A. B[x],
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
lelt: i ≤ j < k,
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
bfalse: ff
Lemmas referenced :
subtype_rel_sets,
bool_wf,
subtype_rel_transitivity,
isect2_subtype_rel2,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_formula_prop_or_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
intformor_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
isect2_subtype_rel3,
equal-wf-T-base,
or_wf,
isect2_wf,
exists_wf,
int_seg_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
lambdaEquality,
cumulativity,
productEquality,
intEquality,
setElimination,
rename,
baseClosed,
applyEquality,
setEquality,
productElimination,
dependent_pairFormation,
unionElimination,
equalityElimination,
dependent_set_memberEquality,
independent_isectElimination,
inlFormation,
independent_pairFormation,
dependent_functionElimination,
int_eqEquality,
voidElimination,
voidEquality,
computeAll,
lambdaFormation
Latex:
Monotone(T.step-function-example(T))
Date html generated:
2016_05_15-PM-10_11_46
Last ObjectModification:
2016_01_16-PM-04_10_15
Theory : eval!all
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