Nuprl Lemma : real_term_value_wf
∀[f:ℤ ⟶ ℝ]. ∀[t:int_term()]. (real_term_value(f;t) ∈ ℝ)
Proof
Definitions occuring in Statement :
real_term_value: real_term_value(f;t),
real: ℝ,
int_term: int_term(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real_term_value: real_term_value(f;t),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
int_term_ind_wf_simple,
real_wf,
int-to-real_wf,
radd_wf,
int_term_wf,
rsub_wf,
rmul_wf,
rminus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
intEquality,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality
Latex:
\mforall{}[f:\mBbbZ{} {}\mrightarrow{} \mBbbR{}]. \mforall{}[t:int\_term()]. (real\_term\_value(f;t) \mmember{} \mBbbR{})
Date html generated:
2017_10_02-PM-07_17_48
Last ObjectModification:
2017_04_02-PM-00_35_46
Theory : reals
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