Nuprl Lemma : pimp_wf
∀[left,right:formula()]. (pimp(left;right) ∈ formula())
Proof
Definitions occuring in Statement :
pimp: pimp(left;right),
formula: formula(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
formula: formula(),
pimp: pimp(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,
formulaco_size: formulaco_size(p),
formula_size: formula_size(p),
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 :
formulaco-ext,
formulaco_wf,
ifthenelse_wf,
eq_atom_wf,
add_nat_wf,
false_wf,
le_wf,
formula_size_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
equal_wf,
has-value_wf-partial,
formulaco_size_wf,
formula_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality,
tokenEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
instantiate,
isectElimination,
universeEquality,
atomEquality,
productEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
independent_isectElimination,
intEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[left,right:formula()]. (pimp(left;right) \mmember{} formula())
Date html generated:
2018_05_21-PM-08_48_56
Last ObjectModification:
2017_07_26-PM-06_11_58
Theory : general
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