Nuprl Lemma : C_Void_wf
C_Void() ∈ C_TYPE()
Proof
Definitions occuring in Statement :
C_Void: C_Void(),
C_TYPE: C_TYPE(),
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
C_TYPE: C_TYPE(),
C_Void: C_Void(),
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
ext-eq: A ≡ B,
and: P ∧ Q,
C_TYPEco_size: C_TYPEco_size(p),
has-value: (a)↓,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
C_TYPEco-ext,
it_wf,
unit_wf2,
ifthenelse_wf,
eq_atom_wf,
list_wf,
C_TYPEco_wf,
nat_wf,
false_wf,
le_wf,
has-value_wf_base,
set_subtype_base,
int_subtype_base,
is-exception_wf,
has-value_wf-partial,
set-value-type,
int-value-type,
C_TYPEco_size_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality,
tokenEquality,
applyEquality,
thin,
lambdaEquality,
hypothesisEquality,
sqequalHypSubstitution,
instantiate,
isectElimination,
universeEquality,
productEquality,
atomEquality,
voidEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
divergentSqle,
sqleReflexivity,
intEquality,
independent_isectElimination,
because_Cache,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
C\_Void() \mmember{} C\_TYPE()
Date html generated:
2016_05_16-AM-08_44_33
Last ObjectModification:
2015_12_28-PM-06_58_13
Theory : C-semantics
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