Nuprl Lemma : intformimplies_wf
∀[left,right:int_formula()]. (left "=>" right ∈ int_formula())
Proof
Definitions occuring in Statement :
intformimplies: left "=>" right,
int_formula: int_formula(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_formula: int_formula(),
intformimplies: left "=>" right,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
int_formulaco_size: int_formulaco_size(p),
int_formula_size: int_formula_size(p),
pi1: fst(t),
pi2: snd(t),
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],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_formulaco-ext,
ifthenelse_wf,
eq_atom_wf,
int_term_wf,
int_formulaco_wf,
add_nat_wf,
istype-void,
le_wf,
int_formula_size_wf,
value-type-has-value,
nat_wf,
set-value-type,
istype-int,
int-value-type,
has-value_wf-partial,
int_formulaco_size_wf,
int_formula_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
Error :dependent_set_memberEquality_alt,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
Error :dependent_pairEquality_alt,
tokenEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
Error :inhabitedIsType,
hypothesisEquality,
Error :universeIsType,
instantiate,
isectElimination,
universeEquality,
productEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
independent_isectElimination,
intEquality,
Error :lambdaEquality_alt,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[left,right:int\_formula()]. (left "=>" right \mmember{} int\_formula())
Date html generated:
2019_06_20-PM-00_46_24
Last ObjectModification:
2018_10_03-AM-00_45_49
Theory : omega
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