Nuprl Lemma : int_formula_prop_wf
∀[f:ℤ ⟶ ℤ]. ∀[fmla:int_formula()]. (int_formula_prop(f;fmla) ∈ ℙ)
Proof
Definitions occuring in Statement :
int_formula_prop: int_formula_prop(f;fmla),
int_formula: int_formula(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_formula_prop: int_formula_prop(f;fmla),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
and: P ∧ Q,
so_apply: x[s1;s2;s3;s4],
implies: P ⇒ Q
Lemmas referenced :
int_formula_ind_wf_simple,
less_than_wf,
int_term_value_wf,
int_term_wf,
le_wf,
equal_wf,
int_formula_wf,
or_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
because_Cache,
intEquality,
productEquality,
cumulativity,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}]. \mforall{}[fmla:int\_formula()]. (int\_formula\_prop(f;fmla) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-07_07_17
Last ObjectModification:
2015_12_26-PM-01_08_53
Theory : omega
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